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Original
2026-01-01
Modified
2026-02-28
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<p>225 Learners</p>
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<p>263 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 itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in fields like vehicle design, finance, and more. Here, we will discuss the square root of 1329.</p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in fields like vehicle design, finance, and more. Here, we will discuss the square root of 1329.</p>
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<h2>What is the Square Root of 1329?</h2>
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<h2>What is the Square Root of 1329?</h2>
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<p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. 1329 is not a<a>perfect square</a>. The square root of 1329 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √1329, whereas in exponential form it is expressed as (1329)^(1/2). √1329 ≈ 36.454, which is an<a>irrational number</a>because it cannot be expressed as a<a>fraction</a>of two<a>integers</a>.</p>
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<p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. 1329 is not a<a>perfect square</a>. The square root of 1329 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √1329, whereas in exponential form it is expressed as (1329)^(1/2). √1329 ≈ 36.454, which is an<a>irrational number</a>because it cannot be expressed as a<a>fraction</a>of two<a>integers</a>.</p>
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<h2>Finding the Square Root of 1329</h2>
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<h2>Finding the Square Root of 1329</h2>
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<p>The<a>prime factorization</a>method is typically used for perfect square numbers. However, for non-perfect square numbers, methods like long-<a>division</a>and approximation are used. Let us now learn about these methods: </p>
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<p>The<a>prime factorization</a>method is typically used for perfect square numbers. However, for non-perfect square numbers, methods like long-<a>division</a>and approximation are used. Let us now learn about 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 1329 by Long Division Method</h2>
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</ul><h2>Square Root of 1329 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly useful for non-perfect square numbers. Below are the steps to find the<a>square root</a>using the long division method:</p>
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<p>The<a>long division</a>method is particularly useful for non-perfect square numbers. Below are the steps to find the<a>square root</a>using the long division method:</p>
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<p><strong>Step 1:</strong>Begin by grouping the digits of the number starting from the right. For 1329, the groups are 29 and 13.</p>
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<p><strong>Step 1:</strong>Begin by grouping the digits of the number starting from the right. For 1329, the groups are 29 and 13.</p>
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<p><strong>Step 2:</strong>Determine the largest integer n such that n^2 is<a>less than</a>or equal to 13. Here, n is 3, since 3^2 = 9.</p>
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<p><strong>Step 2:</strong>Determine the largest integer n such that n^2 is<a>less than</a>or equal to 13. Here, n is 3, since 3^2 = 9.</p>
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<p><strong>Step 3:</strong>Subtract 9 from 13, leaving a<a>remainder</a>of 4, and bring down the next group, 29, to make it 429.</p>
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<p><strong>Step 3:</strong>Subtract 9 from 13, leaving a<a>remainder</a>of 4, and bring down the next group, 29, to make it 429.</p>
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<p><strong>Step 4:</strong>Double the current<a>quotient</a>(3), making it 6, and use it as the starting digits of the new<a>divisor</a>, 6_. Determine the largest digit x such that 6x * x ≤ 429. Here, x is 6.</p>
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<p><strong>Step 4:</strong>Double the current<a>quotient</a>(3), making it 6, and use it as the starting digits of the new<a>divisor</a>, 6_. Determine the largest digit x such that 6x * x ≤ 429. Here, x is 6.</p>
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<p><strong>Step 5:</strong>Subtract 396 (66 * 6) from 429, leaving a remainder of 33.</p>
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<p><strong>Step 5:</strong>Subtract 396 (66 * 6) from 429, leaving a remainder of 33.</p>
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<p><strong>Step 6:</strong>Bring down pairs of zeros, continuing the long-division process to refine the<a>decimal</a>places.</p>
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<p><strong>Step 6:</strong>Bring down pairs of zeros, continuing the long-division process to refine the<a>decimal</a>places.</p>
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<p><strong>Step 7:</strong>Continue this process until the desired precision is achieved. The square root of 1329 is approximately 36.45.</p>
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<p><strong>Step 7:</strong>Continue this process until the desired precision is achieved. The square root of 1329 is approximately 36.45.</p>
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<h2>Square Root of 1329 by Approximation Method</h2>
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<h2>Square Root of 1329 by Approximation Method</h2>
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<p>The approximation method is a simpler way to find the square root of a number. Here's how to find the square root of 1329 using approximation:</p>
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<p>The approximation method is a simpler way to find the square root of a number. Here's how to find the square root of 1329 using approximation:</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 1329. The smaller perfect square is 1296 (36^2) and the larger is 1369 (37^2). Thus, √1329 is between 36 and 37.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 1329. The smaller perfect square is 1296 (36^2) and the larger is 1369 (37^2). Thus, √1329 is between 36 and 37.</p>
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<p><strong>Step 2:</strong>Use interpolation to estimate the square root. Using approximation, √1329 ≈ 36.454.</p>
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<p><strong>Step 2:</strong>Use interpolation to estimate the square root. Using approximation, √1329 ≈ 36.454.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1329</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1329</h2>
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<p>Students often make mistakes while finding square roots, such as forgetting about negative roots or skipping steps in the long division method. Let's explore some common mistakes in detail.</p>
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<p>Students often make mistakes while finding square roots, such as forgetting about negative roots or skipping steps in the long division method. Let's explore some 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 √1329?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √1329?</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 1765.78 square units.</p>
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<p>The area of the square is approximately 1765.78 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 √1329.</p>
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<p>The side length is given as √1329.</p>
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<p>Area = (√1329)^2 = 1329 square units.</p>
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<p>Area = (√1329)^2 = 1329 square units.</p>
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<p>Therefore, the area of the square box is approximately 1765.78 square units.</p>
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<p>Therefore, the area of the square box is approximately 1765.78 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 measures 1329 square feet. If each of the sides is √1329, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measures 1329 square feet. If each of the sides is √1329, 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>664.5 square feet</p>
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<p>664.5 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The area of the building is 1329 square feet.</p>
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<p>The area of the building is 1329 square feet.</p>
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<p>Half of this area is calculated by dividing by 2. 1329 / 2 = 664.5 square feet.</p>
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<p>Half of this area is calculated by dividing by 2. 1329 / 2 = 664.5 square feet.</p>
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<p>So, half of the building measures 664.5 square feet.</p>
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<p>So, half of the building measures 664.5 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 √1329 × 5.</p>
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<p>Calculate √1329 × 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>182.27</p>
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<p>182.27</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 1329, which is approximately 36.454.</p>
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<p>First, find the square root of 1329, which is approximately 36.454.</p>
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<p>Then multiply by 5. 36.454 × 5 = 182.27.</p>
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<p>Then multiply by 5. 36.454 × 5 = 182.27.</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 (1300 + 29)?</p>
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<p>What will be the square root of (1300 + 29)?</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 36.454.</p>
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<p>The square root is approximately 36.454.</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, calculate the sum (1300 + 29) = 1329.</p>
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<p>To find the square root, calculate the sum (1300 + 29) = 1329.</p>
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<p>Then find the square root of 1329, which is approximately 36.454.</p>
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<p>Then find the square root of 1329, which is approximately 36.454.</p>
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<p>Therefore, the square root of (1300 + 29) is approximately ±36.454.</p>
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<p>Therefore, the square root of (1300 + 29) is approximately ±36.454.</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 ‘l’ is √1329 units and the width ‘w’ is 40 units.</p>
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<p>Find the perimeter of a rectangle if its length ‘l’ is √1329 units and the width ‘w’ is 40 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 152.91 units.</p>
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<p>The perimeter of the rectangle is approximately 152.91 units.</p>
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<h3>Explanation</h3>
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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 of the rectangle = 2 × (length + width).</p>
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<p>Perimeter = 2 × (√1329 + 40) = 2 × (36.454 + 40) = 2 × 76.454 = 152.91 units.</p>
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<p>Perimeter = 2 × (√1329 + 40) = 2 × (36.454 + 40) = 2 × 76.454 = 152.91 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 1329</h2>
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<h2>FAQ on Square Root of 1329</h2>
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<h3>1.What is √1329 in its simplest form?</h3>
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<h3>1.What is √1329 in its simplest form?</h3>
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<p>The simplest form of √1329 is just √1329, as the number is not a perfect square and cannot be simplified further.</p>
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<p>The simplest form of √1329 is just √1329, as the number is not a perfect square and cannot be simplified further.</p>
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<h3>2.Mention the factors of 1329.</h3>
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<h3>2.Mention the factors of 1329.</h3>
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<p>Factors of 1329 include 1, 3, 443, and 1329.</p>
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<p>Factors of 1329 include 1, 3, 443, and 1329.</p>
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<h3>3.Calculate the square of 1329.</h3>
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<h3>3.Calculate the square of 1329.</h3>
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<p>The square of 1329 is calculated as 1329 × 1329 = 1,766,241.</p>
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<p>The square of 1329 is calculated as 1329 × 1329 = 1,766,241.</p>
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<h3>4.Is 1329 a prime number?</h3>
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<h3>4.Is 1329 a prime number?</h3>
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<h3>5.What numbers is 1329 divisible by?</h3>
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<h3>5.What numbers is 1329 divisible by?</h3>
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<p>1329 is divisible by 1, 3, 443, and 1329.</p>
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<p>1329 is divisible by 1, 3, 443, and 1329.</p>
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<h2>Important Glossaries for the Square Root of 1329</h2>
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<h2>Important Glossaries for the Square Root of 1329</h2>
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<ul><li><strong>Square root:</strong>The square root of a number is the value that, when multiplied by itself, gives the original number. Example: The square root of 25 is 5.</li>
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<ul><li><strong>Square root:</strong>The square root of a number is the value that, when multiplied by itself, gives the original number. Example: The square root of 25 is 5.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a fraction of two integers. It has a non-repeating, non-terminating decimal expansion.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a fraction of two integers. It has a non-repeating, non-terminating decimal expansion.</li>
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</ul><ul><li><strong>Long division method:</strong>A technique used to divide two numbers, often employed to find the square root of non-perfect squares.</li>
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</ul><ul><li><strong>Long division method:</strong>A technique used to divide two numbers, often employed to find the square root of non-perfect squares.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method to estimate the square root of a number by identifying nearby perfect squares and interpolating.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method to estimate the square root of a number by identifying nearby perfect squares and interpolating.</li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 144 is a perfect square because it is 12 squared.</li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 144 is a perfect square because it is 12 squared.</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>