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2026-01-01
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2026-02-28
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<p>182 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as engineering, physics, and finance. Here, we will discuss the square root of 4250.</p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as engineering, physics, and finance. Here, we will discuss the square root of 4250.</p>
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<h2>What is the Square Root of 4250?</h2>
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<h2>What is the Square Root of 4250?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 4250 is not a<a>perfect square</a>. The square root of 4250 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √4250, whereas (4250)^(1/2) in the exponential form. √4250 ≈ 65.192, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 4250 is not a<a>perfect square</a>. The square root of 4250 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √4250, whereas (4250)^(1/2) in the exponential form. √4250 ≈ 65.192, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<h2>Finding the Square Root of 4250</h2>
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<h2>Finding the Square Root of 4250</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<ul><li>Prime factorization method</li>
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<ul><li>Prime factorization method</li>
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<li>Long division method</li>
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<li>Long division method</li>
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<li>Approximation method</li>
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<li>Approximation method</li>
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</ul><h2>Square Root of 4250 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 4250 by Prime Factorization Method</h2>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 4250 is broken down into its prime factors.</p>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 4250 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 4250 Breaking it down, we get 2 x 5 x 5 x 17 x 5: 2^1 x 5^3 x 17^1</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 4250 Breaking it down, we get 2 x 5 x 5 x 17 x 5: 2^1 x 5^3 x 17^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 4250. The next step is to make pairs of those prime factors. Since 4250 is not a perfect square, the digits of the number can’t be grouped into pairs.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 4250. The next step is to make pairs of those prime factors. Since 4250 is not a perfect square, the digits of the number can’t be grouped into pairs.</p>
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<p>Therefore, calculating 4250 using prime factorization is not straightforward.</p>
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<p>Therefore, calculating 4250 using prime factorization is not straightforward.</p>
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<h2>Square Root of 4250 by Long Division Method</h2>
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<h2>Square Root of 4250 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>Begin by grouping the digits from right to left. For 4250, we group it as 50 and 42.</p>
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<p><strong>Step 1:</strong>Begin by grouping the digits from right to left. For 4250, we group it as 50 and 42.</p>
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<p><strong>Step 2: F</strong>ind n whose square is ≤ 42. We can say n is 6 because 6 x 6 = 36 which is<a>less than</a>or equal to 42. Now, the<a>quotient</a>is 6. After subtracting 36 from 42, the<a>remainder</a>is 6.</p>
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<p><strong>Step 2: F</strong>ind n whose square is ≤ 42. We can say n is 6 because 6 x 6 = 36 which is<a>less than</a>or equal to 42. Now, the<a>quotient</a>is 6. After subtracting 36 from 42, the<a>remainder</a>is 6.</p>
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<p><strong>Step 3:</strong>Bring down the next pair of digits, 50, to make the new<a>dividend</a>650. Add the old<a>divisor</a>with the same number, 6 + 6 = 12, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down the next pair of digits, 50, to make the new<a>dividend</a>650. Add the old<a>divisor</a>with the same number, 6 + 6 = 12, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>Determine the next digit for the quotient. Consider 12n as the new divisor. We need to find n such that 12n x n ≤ 650. Let n be 5, now 125 x 5 = 625.</p>
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<p><strong>Step 4:</strong>Determine the next digit for the quotient. Consider 12n as the new divisor. We need to find n such that 12n x n ≤ 650. Let n be 5, now 125 x 5 = 625.</p>
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<p><strong>Step 5:</strong>Subtract 625 from 650; the difference is 25. Since the remainder is less than the divisor, we add a decimal point to the quotient and bring down two zeros, making the new dividend 2500.</p>
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<p><strong>Step 5:</strong>Subtract 625 from 650; the difference is 25. Since the remainder is less than the divisor, we add a decimal point to the quotient and bring down two zeros, making the new dividend 2500.</p>
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<p><strong>Step 6:</strong>Consider the new divisor as 130 (after adding the previous quotient digit 5 to 125) and find n such that 130n x n ≤ 2500. Let n be 1, now 130 x 1 = 130.</p>
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<p><strong>Step 6:</strong>Consider the new divisor as 130 (after adding the previous quotient digit 5 to 125) and find n such that 130n x n ≤ 2500. Let n be 1, now 130 x 1 = 130.</p>
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<p><strong>Step 7:</strong>Subtract 130 from 2500 to get 2370. Continue this process to determine more decimal places.</p>
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<p><strong>Step 7:</strong>Subtract 130 from 2500 to get 2370. Continue this process to determine more decimal places.</p>
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<p>So, the square root of √4250 is approximately 65.192.</p>
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<p>So, the square root of √4250 is approximately 65.192.</p>
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<h2>Square Root of 4250 by Approximation Method</h2>
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<h2>Square Root of 4250 by Approximation Method</h2>
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<p>The approximation method is another way to find square roots; it is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 4250 using the approximation method.</p>
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<p>The approximation method is another way to find square roots; it is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 4250 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares around 4250. The closest perfect square below 4250 is 4225 (65^2), and the closest perfect square above 4250 is 4356 (66^2). Therefore, √4250 falls between 65 and 66.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares around 4250. The closest perfect square below 4250 is 4225 (65^2), and the closest perfect square above 4250 is 4356 (66^2). Therefore, √4250 falls between 65 and 66.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (4250 - 4225) / (4356 - 4225) ≈ 0.192 Using the formula, we identified the<a>decimal</a>value of our square root approximation. Add this value to the integer part: 65 + 0.192 = 65.192, so the square root of 4250 is approximately 65.192.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (4250 - 4225) / (4356 - 4225) ≈ 0.192 Using the formula, we identified the<a>decimal</a>value of our square root approximation. Add this value to the integer part: 65 + 0.192 = 65.192, so the square root of 4250 is approximately 65.192.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 4250</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 4250</h2>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's look at a few common mistakes in detail.</p>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's look at a few common mistakes in detail.</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √4250?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √4250?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 4250 square units.</p>
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<p>The area of the square is approximately 4250 square units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The area of a square = side^2.</p>
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<p>The area of a square = side^2.</p>
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<p>The side length is given as √4250.</p>
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<p>The side length is given as √4250.</p>
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<p>Area of the square = side^2 = √4250 x √4250 = 4250.</p>
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<p>Area of the square = side^2 = √4250 x √4250 = 4250.</p>
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<p>Therefore, the area of the square box is approximately 4250 square units.</p>
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<p>Therefore, the area of the square box is approximately 4250 square units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>A square-shaped building measuring 4250 square feet is built; if each of the sides is √4250, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 4250 square feet is built; if each of the sides is √4250, what will be the square feet of half of the building?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>2125 square feet</p>
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<p>2125 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>For a square-shaped building, dividing the area by 2 gives the area of half the building.</p>
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<p>For a square-shaped building, dividing the area by 2 gives the area of half the building.</p>
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<p>Dividing 4250 by 2 = 2125.</p>
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<p>Dividing 4250 by 2 = 2125.</p>
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<p>So half of the building measures 2125 square feet.</p>
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<p>So half of the building measures 2125 square feet.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Calculate √4250 x 5.</p>
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<p>Calculate √4250 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Approximately 325.96</p>
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<p>Approximately 325.96</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 4250, which is approximately 65.192.</p>
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<p>The first step is to find the square root of 4250, which is approximately 65.192.</p>
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<p>Then, multiply 65.192 by 5.</p>
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<p>Then, multiply 65.192 by 5.</p>
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<p>So 65.192 x 5 ≈ 325.96.</p>
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<p>So 65.192 x 5 ≈ 325.96.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>What will be the square root of (4250 + 100)?</p>
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<p>What will be the square root of (4250 + 100)?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 66.</p>
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<p>The square root is approximately 66.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the square root, first calculate the sum of (4250 + 100).</p>
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<p>To find the square root, first calculate the sum of (4250 + 100).</p>
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<p>4250 + 100 = 4350, and then √4350 ≈ 66.</p>
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<p>4250 + 100 = 4350, and then √4350 ≈ 66.</p>
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<p>Therefore, the square root of (4250 + 100) is approximately ±66.</p>
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<p>Therefore, the square root of (4250 + 100) is approximately ±66.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √4250 units and the width ‘w’ is 50 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √4250 units and the width ‘w’ is 50 units.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 230.384 units.</p>
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<p>The perimeter of the rectangle is approximately 230.384 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of a rectangle = 2 × (length + width).</p>
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<p>Perimeter of a rectangle = 2 × (length + width).</p>
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<p>Perimeter = 2 × (√4250 + 50)</p>
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<p>Perimeter = 2 × (√4250 + 50)</p>
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<p>= 2 × (65.192 + 50)</p>
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<p>= 2 × (65.192 + 50)</p>
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<p>= 2 × 115.192</p>
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<p>= 2 × 115.192</p>
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<p>= 230.384 units.</p>
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<p>= 230.384 units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 4250</h2>
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<h2>FAQ on Square Root of 4250</h2>
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<h3>1.What is √4250 in its simplest form?</h3>
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<h3>1.What is √4250 in its simplest form?</h3>
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<p>The prime factorization of 4250 is 2 x 5 x 5 x 17 x 5, so the simplest form of √4250 is √(2 x 5^3 x 17).</p>
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<p>The prime factorization of 4250 is 2 x 5 x 5 x 17 x 5, so the simplest form of √4250 is √(2 x 5^3 x 17).</p>
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<h3>2.Mention the factors of 4250.</h3>
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<h3>2.Mention the factors of 4250.</h3>
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<p>Factors of 4250 are 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850, 2125, and 4250.</p>
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<p>Factors of 4250 are 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850, 2125, and 4250.</p>
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<h3>3.Calculate the square of 4250.</h3>
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<h3>3.Calculate the square of 4250.</h3>
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<p>We get the square of 4250 by multiplying the number by itself, that is 4250 x 4250 = 18,062,500.</p>
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<p>We get the square of 4250 by multiplying the number by itself, that is 4250 x 4250 = 18,062,500.</p>
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<h3>4.Is 4250 a prime number?</h3>
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<h3>4.Is 4250 a prime number?</h3>
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<p>4250 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>4250 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.4250 is divisible by?</h3>
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<h3>5.4250 is divisible by?</h3>
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<p>4250 has several factors, including 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850, 2125, and 4250.</p>
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<p>4250 has several factors, including 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850, 2125, and 4250.</p>
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<h2>Important Glossaries for the Square Root of 4250</h2>
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<h2>Important Glossaries for the Square Root of 4250</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse is √16 = 4. </li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse is √16 = 4. </li>
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<li><strong>Irrational number: A</strong>n irrational number is a number that cannot be expressed as a fraction p/q, where q is not zero and p and q are integers. Example: √2. </li>
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<li><strong>Irrational number: A</strong>n irrational number is a number that cannot be expressed as a fraction p/q, where q is not zero and p and q are integers. Example: √2. </li>
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<li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is typically used in real-world applications, known as the principal square root. </li>
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<li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is typically used in real-world applications, known as the principal square root. </li>
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<li><strong>Prime factorization:</strong>The expression of a number as a product of prime numbers. Example: The prime factorization of 18 is 2 x 3 x 3. </li>
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<li><strong>Prime factorization:</strong>The expression of a number as a product of prime numbers. Example: The prime factorization of 18 is 2 x 3 x 3. </li>
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<li><strong>Decimal approximation:</strong>A method to estimate an irrational square root to a certain number of decimal places. Example: √2 ≈ 1.414.</li>
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<li><strong>Decimal approximation:</strong>A method to estimate an irrational square root to a certain number of decimal places. Example: √2 ≈ 1.414.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>