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

3 <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 is used in fields such as vehicle design, finance, and more. Here, we will discuss the square root of 1252.</p>

4 <h2>What is the Square Root of 1252?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>squaring a<a>number</a>. 1252 is not a<a>perfect square</a>. The square root of 1252 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √1252, whereas in exponential form it is expressed as (1252)^(1/2). √1252 ≈ 35.37983, 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 1252</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not suitable, and methods like<a>long division</a>and approximation are used. Let's explore these 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 1252 by Prime Factorization Method</h2>

12 <p>The prime factorization of a number is the<a>product</a>of its prime<a>factors</a>. Now, let's look at how 1252 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1252 Breaking it down, we get 2 x 2 x 313: 2^2 x 313^1</p>

14 <p><strong>Step 2:</strong>We have found the prime factors of 1252. Since 1252 is not a perfect square, the prime factors cannot be grouped into pairs.</p>

15 <p>Therefore, calculating √1252 using prime factorization alone is not possible.</p>

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18 <h2>Square Root of 1252 by Long Division Method</h2>

17 <h2>Square Root of 1252 by Long Division Method</h2>

19 <p>The long<a>division</a>method is particularly useful for non-perfect square numbers. In this method, we find the closest perfect square number to the given number. Let's 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 useful for non-perfect square numbers. In this method, we find the closest perfect square number to the given number. Let's 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, group the numbers from right to left. For 1252, group it as 52 and 12.</p>

19 <p><strong>Step 1:</strong>To begin, group the numbers from right to left. For 1252, group it as 52 and 12.</p>

21 <p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 12. Here, n is 3 because 3 x 3 = 9, which is less than 12. The<a>quotient</a>is 3, and the<a>remainder</a>is 12 - 9 = 3.</p>

20 <p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 12. Here, n is 3 because 3 x 3 = 9, which is less than 12. The<a>quotient</a>is 3, and the<a>remainder</a>is 12 - 9 = 3.</p>

22 <p><strong>Step 3:</strong>Bring down 52, making the new<a>dividend</a>352. Add the old<a>divisor</a>(3) to itself to form the new divisor, 6.</p>

21 <p><strong>Step 3:</strong>Bring down 52, making the new<a>dividend</a>352. Add the old<a>divisor</a>(3) to itself to form the new divisor, 6.</p>

23 <p><strong>Step 4:</strong>Find n such that 6n x n is less than or equal to 352. Let n = 5. Then, 65 x 5 = 325.</p>

22 <p><strong>Step 4:</strong>Find n such that 6n x n is less than or equal to 352. Let n = 5. Then, 65 x 5 = 325.</p>

24 <p><strong>Step 5:</strong>Subtract 325 from 352, giving a remainder of 27. The quotient becomes 35.</p>

23 <p><strong>Step 5:</strong>Subtract 325 from 352, giving a remainder of 27. The quotient becomes 35.</p>

25 <p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point and bring down 00, making the new dividend 2700.</p>

24 <p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point and bring down 00, making the new dividend 2700.</p>

26 <p><strong>Step 7:</strong>Find n such that 700n x n is less than or equal to 2700. Let n = 3. Then, 703 x 3 = 2109.</p>

25 <p><strong>Step 7:</strong>Find n such that 700n x n is less than or equal to 2700. Let n = 3. Then, 703 x 3 = 2109.</p>

27 <p><strong>Step 8:</strong>Subtract 2109 from 2700, giving a remainder of 591.</p>

26 <p><strong>Step 8:</strong>Subtract 2109 from 2700, giving a remainder of 591.</p>

28 <p><strong>Step 9:</strong>Continue this process until you achieve the desired precision.</p>

27 <p><strong>Step 9:</strong>Continue this process until you achieve the desired precision.</p>

29 <p>The square root of √1252 is approximately 35.38.</p>

28 <p>The square root of √1252 is approximately 35.38.</p>

30 <h2>Square Root of 1252 by Approximation Method</h2>

29 <h2>Square Root of 1252 by Approximation Method</h2>

31 <p>The approximation method is another way to find square roots quickly. Let's find the square root of 1252 using this method.</p>

30 <p>The approximation method is another way to find square roots quickly. Let's find the square root of 1252 using this method.</p>

32 <p><strong>Step 1:</strong>Identify the closest perfect squares around 1252. The smallest perfect square less than 1252 is 1225, and the largest is 1296. Thus, √1252 falls between 35 and 36.</p>

31 <p><strong>Step 1:</strong>Identify the closest perfect squares around 1252. The smallest perfect square less than 1252 is 1225, and the largest is 1296. Thus, √1252 falls between 35 and 36.</p>

33 <p><strong>Step 2:</strong>Use interpolation to approximate: (1252 - 1225) / (1296 - 1225) = 27 / 71 ≈ 0.38. Adding this<a>decimal</a>to the lower integer gives 35 + 0.38 = 35.38, so the square root of 1252 is approximately 35.38.</p>

32 <p><strong>Step 2:</strong>Use interpolation to approximate: (1252 - 1225) / (1296 - 1225) = 27 / 71 ≈ 0.38. Adding this<a>decimal</a>to the lower integer gives 35 + 0.38 = 35.38, so the square root of 1252 is approximately 35.38.</p>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1252</h2>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1252</h2>

35 <p>Students often make mistakes when finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's examine a few common mistakes in detail.</p>

34 <p>Students often make mistakes when finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's examine a few common 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 √1252?</p>

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

39 <p>The area of the square is approximately 1252 square units.</p>

40 <h3>Explanation</h3>

41 <p>The area of a square is calculated as side^2.</p>

42 <p>The side length is given as √1252.</p>

43 <p>Area = (√1252) x (√1252) = 1252.</p>

44 <p>Therefore, the area of the square box is approximately 1252 square units.</p>

45 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

47 <p>A square-shaped building measuring 1252 square feet is built; if each of the sides is √1252, what will be the square feet of half of the building?</p>

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

49 <p>626 square feet</p>

50 <h3>Explanation</h3>

51 <p>To find half of the building's area, simply divide the total area by 2.</p>

52 <p>Dividing 1252 by 2 gives 626.</p>

53 <p>So half of the building measures 626 square feet.</p>

54 <p>Well explained 👍</p>

55 <h3>Problem 3</h3>

56 <p>Calculate √1252 x 5.</p>

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

58 <p>Approximately 176.89915</p>

59 <h3>Explanation</h3>

60 <p>First, find the square root of 1252, which is approximately 35.37983.</p>

61 <p>Then multiply by 5.</p>

62 <p>35.37983 x 5 = 176.89915.</p>

63 <p>Well explained 👍</p>

64 <h3>Problem 4</h3>

65 <p>What will be the square root of (1252 + 48)?</p>

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

67 <p>The square root is 36.</p>

68 <h3>Explanation</h3>

69 <p>First, find the sum of 1252 and 48, which is 1300.</p>

70 <p>The closest perfect square to 1300 is 1296, and √1296 is 36.</p>

71 <p>Therefore, the square root of (1252 + 48) is approximately 36.</p>

72 <p>Well explained 👍</p>

73 <h3>Problem 5</h3>

74 <p>Find the perimeter of the rectangle if its length ‘l’ is √1252 units and the width ‘w’ is 38 units.</p>

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

76 <p>The perimeter of the rectangle is approximately 146.76 units.</p>

77 <h3>Explanation</h3>

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

79 <p>Perimeter = 2 × (√1252 + 38)</p>

80 <p>= 2 × (35.37983 + 38)</p>

81 <p>≈ 2 × 73.37983</p>

82 <p>= 146.76 units.</p>

83 <p>Well explained 👍</p>

84 <h2>FAQ on Square Root of 1252</h2>

85 <h3>1.What is √1252 in its simplest form?</h3>

86 <p>The prime factorization of 1252 is 2 x 2 x 313, so the simplest form of √1252 is √(2 x 2 x 313).</p>

87 <h3>2.Mention the factors of 1252.</h3>

88 <p>Factors of 1252 are 1, 2, 4, 313, 626, and 1252.</p>

89 <h3>3.Calculate the square of 1252.</h3>

90 <p>The square of 1252 is 1252 x 1252 = 1,567,504.</p>

91 <h3>4.Is 1252 a prime number?</h3>

92 <p>1252 is not a<a>prime number</a>, as it has more than two factors.</p>

93 <h3>5.1252 is divisible by?</h3>

94 <p>1252 is divisible by 1, 2, 4, 313, 626, and 1252.</p>

95 <h2>Important Glossaries for the Square Root of 1252</h2>

96 <ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse is the square root, √16 = 4. </li>

97 <li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion. </li>

98 <li><strong>Long division method:</strong>A step-by-step approach to finding square roots, especially for non-perfect squares, involving division and approximation. </li>

99 <li><strong>Approximation method:</strong>A method used to find a close estimate of the square root of a number by identifying nearby perfect squares and interpolating between them. </li>

100 <li><strong>Interpolation:</strong>A mathematical method used to estimate values between two known values, often used in approximation methods for finding square roots.</li>

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

102 <p>▶</p>

103 <h2>Jaskaran Singh Saluja</h2>

104 <h3>About the Author</h3>

105 <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>

106 <h3>Fun Fact</h3>

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