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2026-01-01
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2026-02-28
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<p>260 Learners</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 itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1700.</p>
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<h2>What is the Square Root of 1700?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1700 is not a<a>perfect square</a>. The square root of 1700 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1700, whereas (1700)^(1/2) in the exponential form. √1700 ≈ 41.2311, 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 1700</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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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<li>Long division method</li>
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<li>Approximation method</li>
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</ul><h2>Square Root of 1700 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 1700 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1700 Breaking it down, we get 2 x 2 x 5 x 5 x 17: 2² x 5² x 17</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1700. The second step is to make pairs of those prime factors. Since 1700 is not a perfect square, therefore the digits of the number can’t be grouped in perfect pairs.</p>
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<p>Therefore, calculating 1700 using prime factorization is not straightforward for finding the<a>square root</a>.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 1700 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 square root 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 square root using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1700, we need to group it as 17 and 00.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1700, we need to group it as 17 and 00.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 17. We can say n as ‘4’ because 4 x 4 = 16, which is less than 17. Now the<a>quotient</a>is 4, and after subtracting 16 from 17, the<a>remainder</a>is 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 17. We can say n as ‘4’ because 4 x 4 = 16, which is less than 17. Now the<a>quotient</a>is 4, and after subtracting 16 from 17, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00, which makes the new<a>dividend</a>100. Add the old<a>divisor</a>with the same number 4 + 4 to get 8, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00, which makes the new<a>dividend</a>100. Add the old<a>divisor</a>with the same number 4 + 4 to get 8, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the previous divisor and quotient. Now we get 8n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the previous divisor and quotient. Now we get 8n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 8n x n ≤ 100. Let us consider n as 1, now 81 x 1 = 81.</p>
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<p><strong>Step 5:</strong>The next step is finding 8n x n ≤ 100. Let us consider n as 1, now 81 x 1 = 81.</p>
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<p><strong>Step 6:</strong>Subtract 81 from 100; the difference is 19, and the quotient is 41.</p>
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<p><strong>Step 6:</strong>Subtract 81 from 100; the difference is 19, and the quotient is 41.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1900.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. Try using 412 because 412 x 4 = 1648.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. Try using 412 because 412 x 4 = 1648.</p>
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<p><strong>Step 9:</strong>Subtracting 1648 from 1900, we get the result 252.</p>
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<p><strong>Step 9:</strong>Subtracting 1648 from 1900, we get the result 252.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √1700 is approximately 41.23.</p>
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<p>So the square root of √1700 is approximately 41.23.</p>
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<h2>Square Root of 1700 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1700 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √1700.</p>
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<p>The smallest perfect square less than 1700 is 1600, and the largest perfect square<a>greater than</a>1700 is 1764.</p>
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<p>√1700 falls somewhere between 40 and 42.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is</p>
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<p>(Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square).</p>
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<p>Using the formula (1700 - 1600) ÷ (1764 - 1600) = 100 ÷ 164 ≈ 0.61.</p>
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<p>Using the formula, we identified the<a>decimal</a>part of our square root.</p>
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<p>The next step is adding the value we got initially to the decimal number which is 40 + 0.61 = 40.61, so the square root of 1700 is approximately 40.61.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1700</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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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 √1700?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1700 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side². The side length is given as √1700. Area of the square = side² = √1700 x √1700 = 1700. Therefore, the area of the square box is approximately 1700 square units.</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<p>A square-shaped garden measuring 1700 square meters is built; if each of the sides is √1700, what will be the square meters of half of the garden?</p>
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<p>Okay, lets begin</p>
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<p>850 square meters</p>
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<h3>Explanation</h3>
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<p>We can just divide the given area by 2 as the garden is square-shaped. Dividing 1700 by 2 = we get 850. So half of the garden measures 850 square meters.</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<p>Calculate √1700 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 206.1555</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1700, which is approximately 41.2311. The second step is to multiply 41.2311 by 5. So, 41.2311 x 5 ≈ 206.1555.</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<p>What will be the square root of (1600 + 100)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 42.</p>
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<h3>Explanation</h3>
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<p>To find the square root, we need to find the sum of (1600 + 100). 1600 + 100 = 1700, and then √1700 ≈ 41.2311. Therefore, the square root of (1600 + 100) is approximately ±41.2311.</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √1700 units and the width ‘w’ is 25 units.</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as approximately 132.4622 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√1700 + 25) ≈ 2 × (41.2311 + 25) = 2 × 66.2311 ≈ 132.4622 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1700</h2>
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<h3>1.What is √1700 in its simplest form?</h3>
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<p>The prime factorization of 1700 is 2 x 2 x 5 x 5 x 17, so the simplest form of √1700 = √(2² x 5² x 17).</p>
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<h3>2.Mention the factors of 1700.</h3>
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<p>Factors of 1700 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, and 1700.</p>
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<h3>3.Calculate the square of 1700.</h3>
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<p>We get the square of 1700 by multiplying the number by itself, that is 1700 x 1700 = 2,890,000.</p>
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<h3>4.Is 1700 a prime number?</h3>
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<p>1700 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1700 is divisible by?</h3>
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<p>1700 has many factors; those are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, and 1700.</p>
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<h2>Important Glossaries for the Square Root of 1700</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is √16 = 4. </li>
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<li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers. </li>
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<li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root. </li>
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<li><strong>Prime factorization:</strong>Prime factorization is the process of breaking down a number into its prime factors. </li>
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<li><strong>Approximation method:</strong>The approximation method is a technique used to find an approximate value of a square root of a non-perfect square number.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<h2>Jaskaran Singh Saluja</h2>
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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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<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>