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Original
2026-01-01
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2026-02-28
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<p>226 Learners</p>
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<p>INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034</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 have applications in fields like vehicle design and finance. Here, we will discuss the square root of 864.</p>
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<p>SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)</p>
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<h2>What is the Square Root of 864?</h2>
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<p>USA - 251, Little Falls Drive, Wilmington, Delaware 19808</p>
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<p>The<a>square</a>root is the inverse operation<a>of</a>squaring a<a>number</a>. 864 is not a<a>perfect square</a>. The square root of 864 can be expressed in both radical and exponential forms. In radical form, it is expressed as √864, whereas in<a>exponential form</a>, it is (864)^(1/2). The approximate value of √864 is 29.39388, which is an<a>irrational number</a>because it cannot be expressed as a<a>fraction</a>of two integers, p/q, where q ≠ 0.</p>
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<p>VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City</p>
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<h2>Finding the Square Root of 864</h2>
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<p>VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam</p>
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<p>For perfect squares, the<a>prime factorization</a>method is used. However, for non-perfect squares like 864, methods such as<a>long division</a>and approximation are more suitable. Let us explore these methods:</p>
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<p>UAE - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates</p>
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<ul><li>Prime factorization method</li>
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<p>UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom</p>
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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 864 by Prime Factorization Method</h2>
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<p>The prime factorization of a number involves expressing it as a<a>product</a>of<a>prime numbers</a>. Let's break down 864 into its prime<a>factors</a>:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 864</p>
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<p>Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3:<a>2^5</a>× 3^3</p>
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<p><strong>Step 2:</strong>Pair the prime factors. Since 864 is not a perfect square, there will be unpaired factors. Therefore, calculating √864 using prime factorization directly is not feasible.</p>
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<h3>Explore Our Programs</h3>
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<p>No Courses Available</p>
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<h2>Square Root of 864 by Long Division Method</h2>
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<p>The long<a>division</a>method is particularly useful for non-perfect square numbers. This method involves finding the<a>square root</a>step by step:</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left. For 864, group it as 64 and 8.</p>
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<p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 8. Here, n = 2 since 2 × 2 = 4 ≤ 8. Subtract 4 from 8 to get a<a>remainder</a>of 4. Bring down 64 to form 464.</p>
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<p><strong>Step 3:</strong>Double the<a>quotient</a>(2 in this case) to get 4. The new<a>divisor</a>is 4x, and we need to find x such that 4x × x ≤ 464.</p>
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<p><strong>Step 4:</strong>Choose x = 7, since 47 × 7 = 329. Subtract 329 from 464 to get 135.</p>
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<p><strong>Step 5:</strong>Add a<a>decimal</a>point and bring down 00 to make it 13500.</p>
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<p><strong>Step 6:</strong>Continue the process to get a more precise approximation, continuing until you reach the desired accuracy.</p>
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<p>Thus, the square root of 864 is approximately 29.39.</p>
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<h2>Square Root of 864 by Approximation Method</h2>
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<p>The approximation method is an easy way to estimate square roots. Here's how to find the square root of 864 using this method:</p>
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<p><strong>Step 1:</strong>Identify the perfect squares closest to 864. The smaller perfect square is 841 (√841 = 29) and the larger is 900 (√900 = 30). So √864 lies between 29 and 30.</p>
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<p><strong>Step 2:</strong>Use the<a>formula</a>to approximate: (Given number - smaller perfect square) ÷ (Larger perfect square - smaller perfect square) (864 - 841) ÷ (900 - 841) = 23 ÷ 59 ≈ 0.39</p>
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<p><strong>Step 3:</strong>Add this decimal to the smaller root: 29 + 0.39 = 29.39</p>
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<p>Therefore, the approximate square root of 864 is 29.39.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 864</h2>
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<p>Students often make mistakes while finding square roots, such as ignoring the negative square root or skipping steps in the long division method. Here are some common mistakes and how to avoid them:</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 √864?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 864 square units.</p>
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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 side length is given as √864.</p>
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<p>Area = (√864) × (√864) = 864 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 864 square feet is built; if each of the sides is √864, 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>432 square feet</p>
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<h3>Explanation</h3>
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<p>Since the building is square-shaped, we can divide the total area by 2 to find half.</p>
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<p>Dividing 864 by 2 gives us 432.</p>
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<p>So, half of the building measures 432 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 √864 × 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 146.97</p>
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<h3>Explanation</h3>
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<p>First, find the square root of 864, which is approximately 29.39.</p>
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<p>Then multiply 29.39 by 5.</p>
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<p>So, 29.39 × 5 ≈ 146.97.</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 (864 + 36)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 30.</p>
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<h3>Explanation</h3>
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<p>First, find the sum of (864 + 36). 864 + 36 = 900.</p>
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<p>The square root of 900 is 30.</p>
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<p>Therefore, the square root of (864 + 36) 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 √864 units and the width ‘w’ is 40 units.</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 138.78 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of a rectangle = 2 × (length + width)</p>
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<p>Perimeter = 2 × (√864 + 40) ≈ 2 × (29.39 + 40)</p>
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<p>Perimeter ≈ 2 × 69.39 ≈ 138.78 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 864</h2>
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<h3>1.What is √864 in its simplest form?</h3>
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<p>The prime factorization of 864 is 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. The simplest form of √864 is √(2^5 × 3^3).</p>
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<h3>2.Mention the factors of 864.</h3>
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<p>Factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, and 864.</p>
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<h3>3.Calculate the square of 864.</h3>
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<p>The square of 864 is 864 × 864 = 746496.</p>
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<h3>4.Is 864 a prime number?</h3>
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<p>864 is not a prime number, as it has more than two factors.</p>
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<h3>5.864 is divisible by?</h3>
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<p>864 has many factors and is divisible by 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, and 864.</p>
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<h2>Important Glossaries for the Square Root of 864</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: 4^2 = 16, and the square root of 16 is √16 = 4. </li>
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<li><strong>Irrational number:</strong>A number that cannot be expressed as a simple fraction, with non-repeating decimal expansions. </li>
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<li><strong>Perfect Square:</strong>A number that can be expressed as the square of an integer. For example, 16 is a perfect square because it is 4 × 4. </li>
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<li><strong>Prime Factorization:</strong>Expressing a number as the product of its prime factors. Example: the prime factorization of 864 is 2^5 × 3^3. </li>
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<li><strong>Long Division Method:</strong>A technique used to find the square root of non-perfect squares by dividing the number into groups and calculating iteratively.</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>