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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <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 1372.</p>

4 <h2>What is the Square Root of 1372?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1372 is not a<a>perfect square</a>. The square root of 1372 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1372, whereas (1372)^(1/2) in the exponential form. √1372 ≈ 37.041, 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>

6 <h2>Finding the Square Root of 1372</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the<a>long division</a>method and approximation method are used. Let us now learn the following methods:</p>

8 <ul><li>Prime factorization method</li>

9 <li>Long division method</li>

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 1372 by Prime Factorization Method</h2>

12 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 1372 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1372.</p>

14 <p>Breaking it down, we get 2 x 2 x 343: 2^2 x 7^3.</p>

15 <p><strong>Step 2:</strong>Now we have found the prime factors of 1372. The second step is to make pairs of those prime factors. Since 1372 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1372 using prime factorization is not straightforward.</p>

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18 <h2>Square Root of 1372 by Long Division Method</h2>

17 <h2>Square Root of 1372 by Long Division Method</h2>

19 <p>The long<a>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>

18 <p>The long<a>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>

20 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1372, we can group it as 13 and 72.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1372, we can group it as 13 and 72.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 13. We can say n is 3 because 3 x 3 = 9 is lesser than 13. Now the<a>quotient</a>is 3 after subtracting 13 - 9, and the<a>remainder</a>is 4.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 13. We can say n is 3 because 3 x 3 = 9 is lesser than 13. Now the<a>quotient</a>is 3 after subtracting 13 - 9, and the<a>remainder</a>is 4.</p>

22 <p><strong>Step 3:</strong>Now let us bring down 72, making the new<a>dividend</a>472. Add the old<a>divisor</a>with the same number, 3 + 3, we get 6, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Now let us bring down 72, making the new<a>dividend</a>472. Add the old<a>divisor</a>with the same number, 3 + 3, we get 6, which will be our new divisor.</p>

23 <p><strong>Step 4:</strong>We need to find a number such that 6n x n ≤ 472. Let us consider n as 7, as 67 x 7 = 469.</p>

22 <p><strong>Step 4:</strong>We need to find a number such that 6n x n ≤ 472. Let us consider n as 7, as 67 x 7 = 469.</p>

24 <p><strong>Step 5:</strong>Subtract 469 from 472, and the difference is 3.</p>

23 <p><strong>Step 5:</strong>Subtract 469 from 472, and the difference is 3.</p>

25 <p><strong>Step 6:</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 300.</p>

24 <p><strong>Step 6:</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 300.</p>

26 <p><strong>Step 7:</strong>The new divisor is 74, because 740 x 4 = 296.</p>

25 <p><strong>Step 7:</strong>The new divisor is 74, because 740 x 4 = 296.</p>

27 <p><strong>Step 8:</strong>Subtracting 296 from 300, we get the remainder 4.</p>

26 <p><strong>Step 8:</strong>Subtracting 296 from 300, we get the remainder 4.</p>

28 <p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>

27 <p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>

29 <p>The quotient is approximately 37.04.</p>

28 <p>The quotient is approximately 37.04.</p>

30 <h2>Square Root of 1372 by Approximation Method</h2>

29 <h2>Square Root of 1372 by Approximation Method</h2>

31 <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. Let us learn how to find the square root of 1372 using the approximation method.</p>

30 <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. Let us learn how to find the square root of 1372 using the approximation method.</p>

32 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √1372. The smallest perfect square less than 1372 is 1369, and the largest perfect square<a>greater than</a>1372 is 1444. √1372 falls somewhere between 37 and 38.</p>

31 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √1372. The smallest perfect square less than 1372 is 1369, and the largest perfect square<a>greater than</a>1372 is 1444. √1372 falls somewhere between 37 and 38.</p>

33 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1372 - 1369) / (1444 - 1369) = 3 / 75 = 0.04. The square root of 1372 is approximately 37 + 0.04 = 37.04.</p>

32 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1372 - 1369) / (1444 - 1369) = 3 / 75 = 0.04. The square root of 1372 is approximately 37 + 0.04 = 37.04.</p>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1372</h2>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1372</h2>

35 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few of those mistakes in detail.</p>

34 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few of those mistakes in detail.</p>

35 + <h2>Download Worksheets</h2>

36 <h3>Problem 1</h3>

37 <p>Can you help Max find the area of a square box if its side length is given as √138?</p>

38 <p>Okay, lets begin</p>

39 <p>The area of the square is 138 square units.</p>

40 <h3>Explanation</h3>

41 <p>The area of the square = side^2.</p>

42 <p>The side length is given as √138.</p>

43 <p>Area of the square = side^2 = √138 x √138 = 138.</p>

44 <p>Therefore, the area of the square box is 138 square units.</p>

45 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

47 <p>A square-shaped building measuring 1372 square feet is built; if each of the sides is √1372, what will be the square feet of half of the building?</p>

48 <p>Okay, lets begin</p>

49 <p>686 square feet.</p>

50 <h3>Explanation</h3>

51 <p>We can just divide the given area by 2 as the building is square-shaped.</p>

52 <p>Dividing 1372 by 2 = we get 686.</p>

53 <p>So half of the building measures 686 square feet.</p>

54 <p>Well explained 👍</p>

55 <h3>Problem 3</h3>

56 <p>Calculate √1372 x 5.</p>

57 <p>Okay, lets begin</p>

58 <p>185.205</p>

59 <h3>Explanation</h3>

60 <p>The first step is to find the square root of 1372, which is approximately 37.041.</p>

61 <p>The second step is to multiply 37.041 by 5.</p>

62 <p>So, 37.041 x 5 = 185.205.</p>

63 <p>Well explained 👍</p>

64 <h3>Problem 4</h3>

65 <p>What will be the square root of (1369 + 3)?</p>

66 <p>Okay, lets begin</p>

67 <p>The square root is approximately 37.04.</p>

68 <h3>Explanation</h3>

69 <p>To find the square root, we need to find the sum of (1369 + 3). 1369 + 3 = 1372, and then √1372 ≈ 37.04. Therefore, the square root of (1369 + 3) is approximately 37.04.</p>

70 <p>Well explained 👍</p>

71 <h3>Problem 5</h3>

72 <p>Find the perimeter of the rectangle if its length ‘l’ is √1372 units and the width ‘w’ is 38 units.</p>

73 <p>Okay, lets begin</p>

74 <p>We find the perimeter of the rectangle as approximately 150.082 units.</p>

75 <h3>Explanation</h3>

76 <p>Perimeter of the rectangle = 2 × (length + width).</p>

77 <p>Perimeter = 2 × (√1372 + 38) ≈ 2 × (37.041 + 38) ≈ 2 × 75.041 = 150.082 units.</p>

78 <p>Well explained 👍</p>

79 <h2>FAQ on Square Root of 1372</h2>

80 <h3>1.What is √1372 in its simplest form?</h3>

81 <p>The prime factorization of 1372 is 2 x 2 x 7 x 7 x 7, so the simplest form of √1372 = √(2^2 x 7^3).</p>

82 <h3>2.Mention the factors of 1372.</h3>

83 <p>Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, and 1372.</p>

84 <h3>3.Calculate the square of 1372.</h3>

85 <p>We get the square of 1372 by multiplying the number by itself, that is 1372 x 1372 = 1,882,384.</p>

86 <h3>4.Is 1372 a prime number?</h3>

87 <p>1372 is not a<a>prime number</a>, as it has more than two factors.</p>

88 <h3>5.1372 is divisible by?</h3>

89 <p>1372 has several factors; those are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, and 1372.</p>

90 <h2>Important Glossaries for the Square Root of 1372</h2>

91 <ul><li><strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, since 4 x 4 = 16.</li>

92 </ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written as a simple fraction - that is, it cannot be expressed as a ratio of two integers.</li>

93 </ul><ul><li><strong>Principal square root</strong>: A number has both positive and negative square roots. The principal square root is the non-negative square root of a number.</li>

94 </ul><ul><li><strong>Prime factorization:</strong>Breaking down a composite number into its prime factors. For example, the prime factorization of 1372 is 2 x 2 x 7 x 7 x 7.</li>

95 </ul><ul><li><strong>Decimal:</strong>A decimal is a number that consists of a whole number and a fractional part separated by a decimal point. For example, 37.041 is a decimal number.</li>

96 </ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

97 <p>▶</p>

98 <h2>Jaskaran Singh Saluja</h2>

99 <h3>About the Author</h3>

100 <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>

101 <h3>Fun Fact</h3>

102 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>