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2026-01-01
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2026-02-28
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<p>200 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 the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 1378.</p>
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<h2>What is the Square Root of 1378?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1378 is not a<a>perfect square</a>. The square root of 1378 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √1378, whereas (1378)^(1/2) in the exponential form. √1378 ≈ 37.122, 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 1378</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 used for non-perfect square numbers where the long-<a>division</a>method and approximation method are used. 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 1378 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 1378 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1378 1378 can be broken down as 2 x 689. Further breaking down 689, we get 689 = 13 x 53. Therefore, 1378 = 2 x 13 x 53.</p>
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<p><strong>Step 2</strong>: Now we found out the prime factors of 1378. The second step is to make pairs of those prime factors. Since 1378 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √1378 using prime factorization does not yield an exact value.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 1378 by Long Division Method</h2>
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<p>The<a>long 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<a>long 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 1378, we need to group it as 78 and 13.</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 1378, we need to group it as 78 and 13.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 13. We can say n is ‘3’ because 3^2 = 9 is<a>less than</a>13. Now the<a>quotient</a>is 3. Subtracting 9 from 13, the<a>remainder</a>is 4.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 13. We can say n is ‘3’ because 3^2 = 9 is<a>less than</a>13. Now the<a>quotient</a>is 3. Subtracting 9 from 13, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Now let us bring down 78, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 78, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, 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 quotient. Now we get 6n as the new divisor; 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 quotient. Now we get 6n as the new divisor; we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n x n ≤ 478. Let us consider n as 7. Now 67 x 7 = 469.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n x n ≤ 478. Let us consider n as 7. Now 67 x 7 = 469.</p>
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<p><strong>Step 6</strong>: Subtract 469 from 478; the difference is 9, and the quotient is 37.</p>
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<p><strong>Step 6</strong>: Subtract 469 from 478; the difference is 9, and the quotient is 37.</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 900.</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 900.</p>
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<p><strong>Step 8</strong>: Now we need to find the new divisor, which is 371 because 371 x 2 = 742.</p>
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<p><strong>Step 8</strong>: Now we need to find the new divisor, which is 371 because 371 x 2 = 742.</p>
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<p><strong>Step 9:</strong>Subtracting 742 from 900, we get the result 158.</p>
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<p><strong>Step 9:</strong>Subtracting 742 from 900, we get the result 158.</p>
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<p><strong>Step 10:</strong>Now the quotient is 37.12</p>
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<p><strong>Step 10:</strong>Now the quotient is 37.12</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue till 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. Suppose there are no decimal values; continue till the remainder is zero.</p>
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<p>So the square root of √1378 is approximately 37.12.</p>
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<p>So the square root of √1378 is approximately 37.12.</p>
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<h2>Square Root of 1378 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 1378 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1378. The smallest perfect square less than 1378 is 1369 (37^2), and the largest perfect square<a>greater than</a>1378 is 1444 (38^2). √1378 falls somewhere between 37 and 38.</p>
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<p><strong>Step 2</strong>: Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1378 - 1369) ÷ (1444 - 1369) ≈ 0.12. Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number, which is 37 + 0.12 = 37.12, so the square root of 1378 is approximately 37.12.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1378</h2>
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<p>Students make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. 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 √1398?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1398 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √1398.</p>
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<p>Area of the square = side^2 = √1398 x √1398 = 1398.</p>
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<p>Therefore, the area of the square box is 1398 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 garden measuring 1378 square feet is built; if each of the sides is √1378, what will be the square feet of half of the garden?</p>
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<p>Okay, lets begin</p>
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<p>689 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 garden is square-shaped.</p>
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<p>Dividing 1378 by 2, we get 689.</p>
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<p>So half of the garden measures 689 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 √1378 x 4.</p>
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<p>Okay, lets begin</p>
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<p>148.488</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1378, which is approximately 37.122.</p>
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<p>The second step is to multiply 37.122 by 4.</p>
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<p>So 37.122 x 4 ≈ 148.488.</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 (1378 + 22)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 38.</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 (1378 + 22). 1378 + 22 = 1400, and then √1400 ≈ 37.416.</p>
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<p>Therefore, the square root of (1378 + 22) is approximately 37.416.</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 √1378 units and the width ‘w’ is 50 units.</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as approximately 174.244 units.</p>
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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 = 2 × (√1378 + 50) = 2 × (37.122 + 50) ≈ 2 × 87.122 ≈ 174.244 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1378</h2>
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<h3>1.What is √1378 in its simplest form?</h3>
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<p>The prime factorization of 1378 is 2 x 13 x 53, so the simplest radical form of √1378 is √(2 x 13 x 53).</p>
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<h3>2.What are the factors of 1378?</h3>
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<p>Factors of 1378 are 1, 2, 13, 26, 53, 106, 689, and 1378.</p>
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<h3>3.Calculate the square of 1378.</h3>
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<p>We get the square of 1378 by multiplying the number by itself, that is 1378 x 1378 = 1,899,684.</p>
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<h3>4.Is 1378 a prime number?</h3>
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<p>1378 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1378 is divisible by?</h3>
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<p>1378 has several factors; those are 1, 2, 13, 26, 53, 106, 689, and 1378.</p>
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<h2>Important Glossaries for the Square Root of 1378</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that is most commonly used due to its applications in the real world. That is why it is called the principal square root.</li>
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</ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The process of dividing a number into its basic prime factors. For example, the prime factorization of 1378 is 2 x 13 x 53.</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>