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2026-01-01
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2026-02-28
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<p>273 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 a 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 1696.</p>
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<h2>What is the Square Root of 1696?</h2>
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<p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 1696 is not a<a>perfect square</a>. The square root of 1696 is expressed in both radical and exponential forms. In radical form, it is expressed as √1696, whereas in<a>exponential form</a>it is expressed as (1696)^(1/2). The square root of 1696 is approximately 41.1869, 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 1696</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 typically used for non-perfect square numbers, where the<a>long division</a>method and approximation method are preferred. 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 1696 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 1696 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1696 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 53 =<a>2^5</a>x 53</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1696. The second step is to make pairs of those prime factors. Since 1696 is not a perfect square, the digits of the number can’t be fully grouped in pairs.</p>
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<p>Therefore, calculating √1696 using the prime factorization is more complex.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 1696 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 1696, we need to group it as 96 and 16.</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 1696, we need to group it as 96 and 16.</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 16. We can say n as ‘4’ because 4 x 4 = 16. Now the<a>quotient</a>is 4 after subtracting 16 from 16, the<a>remainder</a>is 0.</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 16. We can say n as ‘4’ because 4 x 4 = 16. Now the<a>quotient</a>is 4 after subtracting 16 from 16, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3</strong>: Now let us bring down 96, which is the new<a>dividend</a>. 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 96, which is the new<a>dividend</a>. 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 sum of the dividend and the quotient. Now we get 8n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and the quotient. Now we get 8n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 8n × n ≤ 96. Let us consider n as 1, now 8 x 1 x 1 = 8.</p>
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<p><strong>Step 5:</strong>The next step is finding 8n × n ≤ 96. Let us consider n as 1, now 8 x 1 x 1 = 8.</p>
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<p><strong>Step 6:</strong>Subtract 8 from 96; the difference is 88, and the quotient is 41.</p>
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<p><strong>Step 6:</strong>Subtract 8 from 96; the difference is 88, 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 8800.</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 8800.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. Let us consider n as 9 because 819 x 9 = 7371.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. Let us consider n as 9 because 819 x 9 = 7371.</p>
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<p><strong>Step 9:</strong>Subtracting 7371 from 8800, we get the result 1429.</p>
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<p><strong>Step 9:</strong>Subtracting 7371 from 8800, we get the result 1429.</p>
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<p><strong>Step 10:</strong>Now the quotient is 41.1</p>
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<p><strong>Step 10:</strong>Now the quotient is 41.1</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until 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. If there are no decimal values, continue until the remainder is zero.</p>
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<p>So the square root of √1696 is approximately 41.18.</p>
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<p>So the square root of √1696 is approximately 41.18.</p>
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<h2>Square Root of 1696 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 1696 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √1696.</p>
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<p>The smallest perfect square less than 1696 is 1600, and the closest perfect square<a>greater than</a>1696 is 1764.</p>
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<p>√1696 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 (1696 - 1600) / (1764 - 1600) = 96 / 164 ≈ 0.5854</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 integer part, which is 40 + 0.5854 = 40.5854. So the square root of 1696 is approximately 40.5854.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1696</h2>
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<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. 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 √1296?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 1296 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side^2. The side length is given as √1296. Area of the square = (√1296)^2 = 1296 x 1296 = 1296. Therefore, the area of the square box is 1296 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 1696 square feet is built; if each of the sides is √1696, 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>848 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. Dividing 1696 by 2 = we get 848. So half of the building measures 848 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 √1696 x 5.</p>
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<p>Okay, lets begin</p>
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<p>205.9345</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1696, which is approximately 41.1869. The second step is to multiply 41.1869 by 5. So 41.1869 x 5 ≈ 205.9345.</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 (1296 + 400)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 40.</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 (1296 + 400). 1296 + 400 = 1696, and then √1696 ≈ 41. Therefore, the square root of (1296 + 400) is approximately ±41.</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 √1296 units and the width ‘w’ is 20 units.</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is 88 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√1296 + 20) = 2 × (36 + 20) = 2 × 56 = 112 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1696</h2>
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<h3>1.What is √1696 in its simplest form?</h3>
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<p>The prime factorization of 1696 is 2^5 x 53, so the simplest form of √1696 is √(2^5 x 53).</p>
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<h3>2.Mention the factors of 1696.</h3>
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<p>Factors of 1696 include 1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 848, and 1696.</p>
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<h3>3.Calculate the square of 1696.</h3>
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<p>We get the square of 1696 by multiplying the number by itself, that is 1696 x 1696 = 2,877,216.</p>
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<h3>4.Is 1696 a prime number?</h3>
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<p>1696 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1696 is divisible by?</h3>
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<p>1696 has many factors; those are 1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 848, and 1696.</p>
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<h2>Important Glossaries for the Square Root of 1696</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse operation is the square root: √16 = 4. </li>
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<li><strong>Irrational number:</strong>An irrational number is a number that cannot be expressed as a simple fraction; it's a decimal that goes on forever without repeating. </li>
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<li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 36 is a perfect square because it is 6^2. </li>
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<li><strong>Decimal:</strong>A decimal is a fraction written in a special form. For example, 0.5 is a decimal that represents the fraction 1/2. </li>
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<li><strong>Long division method:</strong>A method used to find the square root of numbers that are not perfect squares by dividing the number into smaller parts.</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>