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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 of squaring a number is finding its square root. The square root concept is used in various fields such as architecture, finance, and engineering. Here, we will discuss the square root of 56.25.</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. The square root concept is used in various fields such as architecture, finance, and engineering. Here, we will discuss the square root of 56.25.</p>
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<h2>What is the Square Root of 56.25?</h2>
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<h2>What is the Square Root of 56.25?</h2>
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<p>The<a>square</a>root is the inverse operation<a>of</a>squaring a<a>number</a>. 56.25 is a<a>perfect square</a>. The square root of 56.25 can be expressed in both radical and exponential forms. In radical form, it is expressed as √56.25, whereas in<a>exponential form</a>it is expressed as (56.25)^(1/2). The square root of 56.25 is 7.5, which is a<a>rational number</a>because it can be expressed as a<a>fraction</a>, 15/2.</p>
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<p>The<a>square</a>root is the inverse operation<a>of</a>squaring a<a>number</a>. 56.25 is a<a>perfect square</a>. The square root of 56.25 can be expressed in both radical and exponential forms. In radical form, it is expressed as √56.25, whereas in<a>exponential form</a>it is expressed as (56.25)^(1/2). The square root of 56.25 is 7.5, which is a<a>rational number</a>because it can be expressed as a<a>fraction</a>, 15/2.</p>
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<h2>Finding the Square Root of 56.25</h2>
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<h2>Finding the Square Root of 56.25</h2>
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<p>To find the<a>square root</a>of perfect squares, methods such as<a>prime factorization</a>,<a>long division</a>, and direct calculation can be used. Since 56.25 is a perfect square, we will explore the following methods: </p>
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<p>To find the<a>square root</a>of perfect squares, methods such as<a>prime factorization</a>,<a>long division</a>, and direct calculation can be used. Since 56.25 is a perfect square, we will explore the following methods: </p>
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<ul><li>Prime factorization method </li>
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<ul><li>Prime factorization method </li>
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<li>Long division method </li>
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<li>Long division method </li>
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<li>Direct calculation method</li>
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<li>Direct calculation method</li>
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</ul><h3>Square Root of 56.25 by Prime Factorization Method</h3>
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</ul><h3>Square Root of 56.25 by Prime Factorization Method</h3>
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<p>The prime factorization method involves breaking down a number into its prime<a>factors</a>. Let's see how 56.25 is broken down into its prime factors.</p>
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<p>The prime factorization method involves breaking down a number into its prime<a>factors</a>. Let's see how 56.25 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Express 56.25 as a fraction: 5625/100.</p>
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<p><strong>Step 1:</strong>Express 56.25 as a fraction: 5625/100.</p>
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<p><strong>Step 2:</strong>Find the prime factors of 5625: 5625 = 3² × 5⁴.</p>
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<p><strong>Step 2:</strong>Find the prime factors of 5625: 5625 = 3² × 5⁴.</p>
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<p><strong>Step 3:</strong>Find the prime factors of 100: 100 = 2² × 5².</p>
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<p><strong>Step 3:</strong>Find the prime factors of 100: 100 = 2² × 5².</p>
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<p><strong>Step 4:</strong>Simplify the fraction: (3² × 5⁴) / (2² × 5²) = (3² × 5²) / 2².</p>
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<p><strong>Step 4:</strong>Simplify the fraction: (3² × 5⁴) / (2² × 5²) = (3² × 5²) / 2².</p>
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<p><strong>Step 5:</strong>Find the square root: √56.25 = 7.5.</p>
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<p><strong>Step 5:</strong>Find the square root: √56.25 = 7.5.</p>
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<h2>Square Root of 56.25 by Long Division Method</h2>
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<h2>Square Root of 56.25 by Long Division Method</h2>
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<p>The long<a>division</a>method is suited for finding the square root of both perfect and non-perfect squares. Let's learn how to find the square root using the long division method, step by step.</p>
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<p>The long<a>division</a>method is suited for finding the square root of both perfect and non-perfect squares. Let's 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>Begin by pairing the digits from right to left. For 56.25, group it as 56 and 25.</p>
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<p><strong>Step 1:</strong>Begin by pairing the digits from right to left. For 56.25, group it as 56 and 25.</p>
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<p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 56. This number is 7, since 7 × 7 = 49.</p>
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<p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 56. This number is 7, since 7 × 7 = 49.</p>
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<p><strong>Step 3:</strong>Subtract 49 from 56 to get the<a>remainder</a>7. Bring down 25 to make it 725.</p>
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<p><strong>Step 3:</strong>Subtract 49 from 56 to get the<a>remainder</a>7. Bring down 25 to make it 725.</p>
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<p><strong>Step 4:</strong>Double the<a>quotient</a>7 to get 14 and<a>set</a>it as the<a>divisor</a>'s leading digit.</p>
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<p><strong>Step 4:</strong>Double the<a>quotient</a>7 to get 14 and<a>set</a>it as the<a>divisor</a>'s leading digit.</p>
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<p><strong>Step 5:</strong>Find a digit X such that 14X × X is less than or equal to 725. The suitable X is 5, as 145 × 5 = 725.</p>
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<p><strong>Step 5:</strong>Find a digit X such that 14X × X is less than or equal to 725. The suitable X is 5, as 145 × 5 = 725.</p>
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<p><strong>Step 6:</strong>Subtract 725 from 725 to get a remainder of 0.</p>
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<p><strong>Step 6:</strong>Subtract 725 from 725 to get a remainder of 0.</p>
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<p>Thus, the square root of 56.25 is 7.5.</p>
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<p>Thus, the square root of 56.25 is 7.5.</p>
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<h2>Square Root of 56.25 by Direct Calculation Method</h2>
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<h2>Square Root of 56.25 by Direct Calculation Method</h2>
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<p>The direct calculation method is efficient for perfect squares. Let's find the square root of 56.25 using direct calculation.</p>
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<p>The direct calculation method is efficient for perfect squares. Let's find the square root of 56.25 using direct calculation.</p>
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<p><strong>Step 1:</strong>Recognize that 56.25 is a perfect square, as it can be written as (7.5)².</p>
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<p><strong>Step 1:</strong>Recognize that 56.25 is a perfect square, as it can be written as (7.5)².</p>
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<p><strong>Step 2:</strong>Therefore, √56.25 = 7.5.</p>
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<p><strong>Step 2:</strong>Therefore, √56.25 = 7.5.</p>
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<h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 56.25</h2>
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<h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 56.25</h2>
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<p>Students often make errors when calculating square roots, like ignoring the decimal point or miscalculating the square of numbers. Let's explore common mistakes and how to address them.</p>
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<p>Students often make errors when calculating square roots, like ignoring the decimal point or miscalculating the square of numbers. Let's explore common mistakes and how to address them.</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 Ella find the area of a square box if its side length is given as √56.25?</p>
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<p>Can you help Ella find the area of a square box if its side length is given as √56.25?</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 56.25 square units.</p>
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<p>The area of the square is 56.25 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 the square = side².</p>
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<p>The area of the square = side².</p>
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<p>The side length is given as √56.25.</p>
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<p>The side length is given as √56.25.</p>
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<p>Area of the square = side² = √56.25 × √56.25 = 7.5 × 7.5 = 56.25.</p>
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<p>Area of the square = side² = √56.25 × √56.25 = 7.5 × 7.5 = 56.25.</p>
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<p>Therefore, the area of the square box is 56.25 square units.</p>
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<p>Therefore, the area of the square box is 56.25 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 plot measuring 56.25 square meters is divided into two equal parts; what is the area of each part?</p>
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<p>A square-shaped plot measuring 56.25 square meters is divided into two equal parts; what is the area of each part?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>28.125 square meters</p>
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<p>28.125 square meters</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The plot is square-shaped, and its area is 56.25 square meters.</p>
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<p>The plot is square-shaped, and its area is 56.25 square meters.</p>
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<p>Dividing the area by 2 gives 28.125 square meters for each part.</p>
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<p>Dividing the area by 2 gives 28.125 square meters for each part.</p>
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<p>So, each part measures 28.125 square meters.</p>
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<p>So, each part measures 28.125 square meters.</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 √56.25 × 3.</p>
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<p>Calculate √56.25 × 3.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>22.5</p>
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<p>22.5</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 56.25, which is 7.5.</p>
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<p>The first step is to find the square root of 56.25, which is 7.5.</p>
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<p>The second step is to multiply 7.5 with 3.</p>
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<p>The second step is to multiply 7.5 with 3.</p>
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<p>So, 7.5 × 3 = 22.5.</p>
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<p>So, 7.5 × 3 = 22.5.</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 (50 + 6.25)?</p>
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<p>What will be the square root of (50 + 6.25)?</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 7.5</p>
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<p>The square root is 7.5</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, we need to find the sum of (50 + 6.25). 50 + 6.25 = 56.25, and then √56.25 = 7.5.</p>
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<p>To find the square root, we need to find the sum of (50 + 6.25). 50 + 6.25 = 56.25, and then √56.25 = 7.5.</p>
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<p>Therefore, the square root of (50 + 6.25) is ±7.5.</p>
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<p>Therefore, the square root of (50 + 6.25) is ±7.5.</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 √56.25 units and the width ‘w’ is 20 units.</p>
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<p>Find the perimeter of a rectangle if its length ‘l’ is √56.25 units and the width ‘w’ is 20 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 55 units.</p>
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<p>The perimeter of the rectangle is 55 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 × (√56.25 + 20) = 2 × (7.5 + 20) = 2 × 27.5 = 55 units.</p>
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<p>Perimeter = 2 × (√56.25 + 20) = 2 × (7.5 + 20) = 2 × 27.5 = 55 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 56.25</h2>
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<h2>FAQ on Square Root of 56.25</h2>
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<h3>1.What is √56.25 in its simplest form?</h3>
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<h3>1.What is √56.25 in its simplest form?</h3>
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<p>The prime factorization of 56.25 involves 5625/100 = (3² × 5⁴) / (2² × 5²). The simplest form of √56.25 is 7.5.</p>
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<p>The prime factorization of 56.25 involves 5625/100 = (3² × 5⁴) / (2² × 5²). The simplest form of √56.25 is 7.5.</p>
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<h3>2.Mention the factors of 56.25.</h3>
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<h3>2.Mention the factors of 56.25.</h3>
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<p>Factors of 56.25 (as a<a>whole number</a>) are 1, 3, 5, 9, 15, 25, 45, 75, 225, 375, 1125, and 5625.</p>
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<p>Factors of 56.25 (as a<a>whole number</a>) are 1, 3, 5, 9, 15, 25, 45, 75, 225, 375, 1125, and 5625.</p>
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<h3>3.Calculate the square of 56.25.</h3>
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<h3>3.Calculate the square of 56.25.</h3>
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<p>The square of 56.25 is obtained by multiplying the number by itself, that is 56.25 × 56.25 = 3164.0625.</p>
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<p>The square of 56.25 is obtained by multiplying the number by itself, that is 56.25 × 56.25 = 3164.0625.</p>
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<h3>4.Is 56.25 a perfect square?</h3>
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<h3>4.Is 56.25 a perfect square?</h3>
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<p>Yes, 56.25 is a perfect square, as it can be expressed as (7.5)².</p>
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<p>Yes, 56.25 is a perfect square, as it can be expressed as (7.5)².</p>
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<h3>5.56.25 is divisible by?</h3>
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<h3>5.56.25 is divisible by?</h3>
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<p>56.25 is divisible by 1, 3, 5, 9, 15, 25, 45, 75, 225, 375, 1125, and 5625.</p>
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<p>56.25 is divisible by 1, 3, 5, 9, 15, 25, 45, 75, 225, 375, 1125, and 5625.</p>
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<h2>Important Glossaries for the Square Root of 56.25</h2>
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<h2>Important Glossaries for the Square Root of 56.25</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, if 4² = 16, then the square root of 16 is √16 = 4 </li>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, if 4² = 16, then the square root of 16 is √16 = 4 </li>
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<li><strong>Rational number:</strong>A rational number is any number that can be expressed as the fraction p/q, where p and q are integers and q ≠ 0. </li>
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<li><strong>Rational number:</strong>A rational number is any number that can be expressed as the fraction p/q, where p and q are integers and q ≠ 0. </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, 49 is a perfect square because it is 7². </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, 49 is a perfect square because it is 7². </li>
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<li><strong>Decimal:</strong>A decimal is a number that includes a fractional part separated from the integer part by a decimal point, such as 7.5. </li>
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<li><strong>Decimal:</strong>A decimal is a number that includes a fractional part separated from the integer part by a decimal point, such as 7.5. </li>
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<li><strong>Long division:</strong>A method used to divide larger numbers that involves several steps of division, multiplication, and subtraction.</li>
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<li><strong>Long division:</strong>A method used to divide larger numbers that involves several steps of division, multiplication, and subtraction.</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>