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2026-01-01
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2026-02-28
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<p>319 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 the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 890.</p>
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<h2>What is the Square Root of 890?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 890 is not a<a>perfect square</a>. The square root of 890 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √890, whereas 890^(1/2) in the exponential form. √890 ≈ 29.8329, 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 890</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<a>long 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 890 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 890 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 890 Breaking it down, we get 2 x 5 x 89: 2^1 x 5^1 x 89^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 890. The second step is to make pairs of those prime factors. Since 890 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 890 using prime factorization is impossible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 890 by Long Division Method</h2>
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<p>The long<a>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 long<a>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>To begin with, we need to group the numbers from right to left. In the case of 890, we need to group it as 90 and 8.</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 890, we need to group it as 90 and 8.</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 8. We can say n as ‘2’ because 2 x 2 = 4 is less than 8. Now the<a>quotient</a>is 2, and after subtracting 8 - 4, the<a>remainder</a>is 4.</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 8. We can say n as ‘2’ because 2 x 2 = 4 is less than 8. Now the<a>quotient</a>is 2, and after subtracting 8 - 4, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Now let us bring down 90, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2; we get 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 90, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2; we get 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 490. Let us consider n as 9. Now 49 x 9 = 441.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 490. Let us consider n as 9. Now 49 x 9 = 441.</p>
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<p><strong>Step 6:</strong>Subtract 490 from 441; the difference is 49, and the quotient is 29.</p>
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<p><strong>Step 6:</strong>Subtract 490 from 441; the difference is 49, and the quotient is 29.</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 4900.</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 4900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 598, because 598 x 8 = 4784.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 598, because 598 x 8 = 4784.</p>
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<p><strong>Step 9:</strong>Subtracting 4784 from 4900, we get the result 116. Step 10: Now the quotient is 29.8</p>
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<p><strong>Step 9:</strong>Subtracting 4784 from 4900, we get the result 116. Step 10: Now the quotient is 29.8</p>
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<p><strong>Step 11:</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 11:</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 √890 is approximately 29.83.</p>
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<p>So the square root of √890 is approximately 29.83.</p>
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<h2>Square Root of 890 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 890 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √890.</p>
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<p>The smallest perfect square less than 890 is 841, and the largest perfect square<a>greater than</a>890 is 900.</p>
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<p>√890 falls somewhere between 29 and 30.</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>Going by the formula (890 - 841) / (900 - 841) ≈ 0.83</p>
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<p>Using the formula, we identified the<a>decimal</a>point 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 29 + 0.83 = 29.83, so the square root of 890 is approximately 29.83.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 890</h2>
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<p>Students do make mistakes while finding the square root, like 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 √890?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 790.5281 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √890.</p>
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<p>Area of the square = side^2 = √890 x √890 ≈ 29.83 × 29.83 ≈ 890.</p>
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<p>Therefore, the area of the square box is approximately 890 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 building measuring 890 square feet is built; if each of the sides is √890, 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>445 square feet</p>
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<h3>Explanation</h3>
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<p>We can just divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 890 by 2 = 445.</p>
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<p>So half of the building measures 445 square feet.</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<p>Calculate √890 × 4.</p>
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<p>Okay, lets begin</p>
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<p>119.328</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 890, which is approximately 29.83.</p>
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<p>The second step is to multiply 29.83 by 4. So 29.83 × 4 ≈ 119.328.</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 (890 + 10)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 30.</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 (890 + 10). 890 + 10 = 900, and then √900 = 30.</p>
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<p>Therefore, the square root of (890 + 10) is ±30.</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 √890 units and the width ‘w’ is 40 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 139.66 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width).</p>
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<p>Perimeter = 2 × (√890 + 40) = 2 × (29.83 + 40) = 2 × 69.83 ≈ 139.66 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 890</h2>
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<h3>1.What is √890 in its simplest form?</h3>
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<p>The prime factorization of 890 is 2 x 5 x 89, so the simplest form of √890 = √(2 x 5 x 89).</p>
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<h3>2.Mention the factors of 890.</h3>
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<p>Factors of 890 are 1, 2, 5, 10, 89, 178, 445, and 890.</p>
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<h3>3.Calculate the square of 890.</h3>
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<p>We get the square of 890 by multiplying the number by itself, that is 890 x 890 = 792,100.</p>
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<h3>4.Is 890 a prime number?</h3>
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<h3>5.890 is divisible by?</h3>
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<p>890 has several factors; those are 1, 2, 5, 10, 89, 178, 445, and 890.</p>
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<h2>Important Glossaries for the Square Root of 890</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 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>Perfect square:</strong>A perfect square is a number that is the square of an integer. Example: 16 is a perfect square because it is 4^2. </li>
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<li><strong>Decimal:</strong>A decimal is a number that contains a whole number and a fractional part, represented with a decimal point. Example: 7.86, 8.65, and 9.42 are decimals. </li>
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<li><strong>Approximation:</strong>Approximation is a method of finding a value that is close enough to the correct answer, usually with some degree of accuracy.</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>