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2026-01-01
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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 itself, the result is a square. The inverse operation is finding the square root. The concept of square roots is applied in various fields, such as engineering, finance, and physics. Here, we will discuss the square root of 3/2.</p>
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<p>If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The concept of square roots is applied in various fields, such as engineering, finance, and physics. Here, we will discuss the square root of 3/2.</p>
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<h2>What is the Square Root of 3/2?</h2>
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<h2>What is the Square Root of 3/2?</h2>
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<p>The<a>square</a>root is the inverse operation<a>of</a>squaring a<a>number</a>. The number 3/2 is not a<a>perfect square</a>. The square root of 3/2 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √(3/2), whereas (3/2)^(1/2) in exponential form. √(3/2) is an<a>irrational number</a>because it cannot be expressed as a simple<a>fraction</a>of two integers.</p>
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<p>The<a>square</a>root is the inverse operation<a>of</a>squaring a<a>number</a>. The number 3/2 is not a<a>perfect square</a>. The square root of 3/2 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √(3/2), whereas (3/2)^(1/2) in exponential form. √(3/2) is an<a>irrational number</a>because it cannot be expressed as a simple<a>fraction</a>of two integers.</p>
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<h2>Finding the Square Root of 3/2</h2>
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<h2>Finding the Square Root of 3/2</h2>
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<p>For non-perfect square numbers, the<a>prime factorization</a>method is not applicable. Instead, methods like the long-<a>division</a>method and approximation method are used. Let us explore these methods:</p>
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<p>For non-perfect square numbers, the<a>prime factorization</a>method is not applicable. Instead, methods like the long-<a>division</a>method and approximation method are used. Let us explore these methods:</p>
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<ul><li>Long division method</li>
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<ul><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 3/2 by Long Division Method</h2>
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</ul><h2>Square Root of 3/2 by Long Division Method</h2>
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<p>The<a>long division</a>method is useful for finding the square roots of non-perfect square numbers. Here is how we can calculate the<a>square root</a>of 3/2 using this method:</p>
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<p>The<a>long division</a>method is useful for finding the square roots of non-perfect square numbers. Here is how we can calculate the<a>square root</a>of 3/2 using this method:</p>
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<p><strong>Step 1:</strong>Convert the fraction 3/2 to a<a>decimal</a>, which is 1.5.</p>
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<p><strong>Step 1:</strong>Convert the fraction 3/2 to a<a>decimal</a>, which is 1.5.</p>
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<p><strong>Step 2:</strong>Use the long division method to find the square root of 1.5.</p>
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<p><strong>Step 2:</strong>Use the long division method to find the square root of 1.5.</p>
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<p><strong>Step 3:</strong>Group the digits of 1.5, considering it as 150 in the long division format.</p>
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<p><strong>Step 3:</strong>Group the digits of 1.5, considering it as 150 in the long division format.</p>
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<p><strong>Step 4:</strong>Find the largest number whose square is<a>less than</a>or equal to 150.</p>
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<p><strong>Step 4:</strong>Find the largest number whose square is<a>less than</a>or equal to 150.</p>
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<p><strong>Step 5:</strong>Continue the long division process until you reach the desired level of precision.</p>
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<p><strong>Step 5:</strong>Continue the long division process until you reach the desired level of precision.</p>
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<p>The square root of 1.5 is approximately 1.2247, so √(3/2) ≈ 1.2247.</p>
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<p>The square root of 1.5 is approximately 1.2247, so √(3/2) ≈ 1.2247.</p>
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<h2>Square Root of 3/2 by Approximation Method</h2>
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<h2>Square Root of 3/2 by Approximation Method</h2>
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<p>The approximation method is another approach to finding square roots. This method is relatively easy for estimating the square root of a number. Here is how we can find the square root of 3/2 using approximation:</p>
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<p>The approximation method is another approach to finding square roots. This method is relatively easy for estimating the square root of a number. Here is how we can find the square root of 3/2 using approximation:</p>
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<p><strong>Step 1:</strong>Convert the fraction 3/2 to a decimal, which is 1.5.</p>
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<p><strong>Step 1:</strong>Convert the fraction 3/2 to a decimal, which is 1.5.</p>
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<p><strong>Step 2:</strong>Identify two perfect squares between which 1.5 falls. The perfect squares are 1 (1^2) and 4 (2^2), so √1.5 is between 1 and 2.</p>
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<p><strong>Step 2:</strong>Identify two perfect squares between which 1.5 falls. The perfect squares are 1 (1^2) and 4 (2^2), so √1.5 is between 1 and 2.</p>
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<p><strong>Step 3:</strong>Use interpolation to estimate √1.5. The difference between 1.5 and 1 is 0.5, and the difference between 4 and 1 is 3.</p>
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<p><strong>Step 3:</strong>Use interpolation to estimate √1.5. The difference between 1.5 and 1 is 0.5, and the difference between 4 and 1 is 3.</p>
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<p><strong>Step 4:</strong>Calculate the approximate value using interpolation: (1.5 - 1) / (4 - 1) = 0.5 / 3 = 0.1667.</p>
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<p><strong>Step 4:</strong>Calculate the approximate value using interpolation: (1.5 - 1) / (4 - 1) = 0.5 / 3 = 0.1667.</p>
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<p><strong>Step 5:</strong>Add this value to the lower bound of 1 to estimate √1.5 ≈ 1.1667. For more precision, further calculations can be done.</p>
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<p><strong>Step 5:</strong>Add this value to the lower bound of 1 to estimate √1.5 ≈ 1.1667. For more precision, further calculations can be done.</p>
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<p>The square root of 3/2 is approximately 1.2247.</p>
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<p>The square root of 3/2 is approximately 1.2247.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 3/2</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 3/2</h2>
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<p>Students often make errors when calculating square roots, such as neglecting the negative square root or incorrect usage of methods. Let us examine some common mistakes in detail.</p>
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<p>Students often make errors when calculating square roots, such as neglecting the negative square root or incorrect usage of methods. Let us examine some common mistakes in detail.</p>
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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 if its side length is given as √(3/2)?</p>
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<p>Can you help Max find the area of a square if its side length is given as √(3/2)?</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 1.5 square units.</p>
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<p>The area of the square is approximately 1.5 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 = side².</p>
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<p>The area of a square = side².</p>
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<p>The side length is given as √(3/2).</p>
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<p>The side length is given as √(3/2).</p>
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<p>Area of the square = (√(3/2))² = 3/2 ≈ 1.5</p>
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<p>Area of the square = (√(3/2))² = 3/2 ≈ 1.5</p>
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<p>Therefore, the area of the square is 1.5 square units.</p>
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<p>Therefore, the area of the square is 1.5 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 rectangle has an area of 3/2 square units. If one side is √(3/2), what will be the length of the other side?</p>
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<p>A rectangle has an area of 3/2 square units. If one side is √(3/2), what will be the length of the other side?</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 other side is 1 unit.</p>
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<p>The other side is 1 unit.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Area = length × width.</p>
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<p>Area = length × width.</p>
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<p>Given the area is 3/2 and one side is √(3/2), the other side is calculated as (3/2) / √(3/2) = 1.</p>
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<p>Given the area is 3/2 and one side is √(3/2), the other side is calculated as (3/2) / √(3/2) = 1.</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 √(3/2) × 4.</p>
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<p>Calculate √(3/2) × 4.</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 result is approximately 4.898.</p>
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<p>The result is approximately 4.898.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, find the square root of 3/2, which is approximately 1.2247.</p>
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<p>First, find the square root of 3/2, which is approximately 1.2247.</p>
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<p>Then multiply 1.2247 by 4: 1.2247 × 4 ≈ 4.898.</p>
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<p>Then multiply 1.2247 by 4: 1.2247 × 4 ≈ 4.898.</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 is the square root of (1.5 + 0.5)?</p>
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<p>What is the square root of (1.5 + 0.5)?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 1.414.</p>
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<p>The square root is approximately 1.414.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, calculate the sum: 1.5 + 0.5 = 2.</p>
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<p>First, calculate the sum: 1.5 + 0.5 = 2.</p>
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<p>Then find the square root of 2, which is approximately 1.414.</p>
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<p>Then find the square root of 2, which is approximately 1.414.</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 a rectangle if its length is √(3/2) units and the width is 2 units.</p>
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<p>Find the perimeter of a rectangle if its length is √(3/2) units and the width is 2 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 6.4494 units.</p>
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<p>The perimeter of the rectangle is approximately 6.4494 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). Perimeter = 2 × (√(3/2) + 2) ≈ 2 × (1.2247 + 2) ≈ 6.4494 units.</p>
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<p>Perimeter of a rectangle = 2 × (length + width). Perimeter = 2 × (√(3/2) + 2) ≈ 2 × (1.2247 + 2) ≈ 6.4494 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 3/2</h2>
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<h2>FAQ on Square Root of 3/2</h2>
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<h3>1.What is √(3/2) in its simplest form?</h3>
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<h3>1.What is √(3/2) in its simplest form?</h3>
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<h3>2.Is 3/2 a perfect square?</h3>
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<h3>2.Is 3/2 a perfect square?</h3>
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<p>No, 3/2 is not a perfect square because there is no<a>integer</a>that, when squared, equals 3/2.</p>
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<p>No, 3/2 is not a perfect square because there is no<a>integer</a>that, when squared, equals 3/2.</p>
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<h3>3.Calculate the square of 3/2.</h3>
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<h3>3.Calculate the square of 3/2.</h3>
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<p>The square of 3/2 is (3/2)² = 9/4 or 2.25.</p>
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<p>The square of 3/2 is (3/2)² = 9/4 or 2.25.</p>
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<h3>4.Is 3/2 a rational number?</h3>
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<h3>4.Is 3/2 a rational number?</h3>
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<h3>5.What is the decimal representation of 3/2?</h3>
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<h3>5.What is the decimal representation of 3/2?</h3>
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<h2>Important Glossaries for the Square Root of 3/2</h2>
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<h2>Important Glossaries for the Square Root of 3/2</h2>
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<ul><li><strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. Example: The square root of 4 is 2, because 2 × 2 = 4.</li>
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<ul><li><strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. Example: The square root of 4 is 2, because 2 × 2 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction; its decimal form is non-repeating and non-terminating. Example: √2 is irrational.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction; its decimal form is non-repeating and non-terminating. Example: √2 is irrational.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as a fraction with an integer numerator and a non-zero integer denominator. Example: 3/2 is rational.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as a fraction with an integer numerator and a non-zero integer denominator. Example: 3/2 is rational.</li>
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</ul><ul><li><strong>Decimal:</strong>A decimal represents a non-integer number using place value and a decimal point. Example: 1.5 is a decimal representation of 3/2.</li>
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</ul><ul><li><strong>Decimal:</strong>A decimal represents a non-integer number using place value and a decimal point. Example: 1.5 is a decimal representation of 3/2.</li>
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</ul><ul><li><strong>Interpolation:</strong>Interpolation is a method of estimating unknown values that fall between known values. It is used in approximating square roots, like estimating √1.5.</li>
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</ul><ul><li><strong>Interpolation:</strong>Interpolation is a method of estimating unknown values that fall between known values. It is used in approximating square roots, like estimating √1.5.</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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<p>▶</p>
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<p>▶</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>