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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1242.</p>

4 <h2>What is the Square Root of 1242?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 1242 is not a<a>perfect square</a>. The square root of 1242 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √1242, whereas in exponential form it is (1242)^(1/2). √1242 ≈ 35.2293, 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 1242</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 1242 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 1242 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1242 Breaking it down, we get 2 x 3 x 3 x 3 x 23: 2^1 x 3^3 x 23^1</p>

14 <p><strong>Step 2:</strong>Now we have found the prime factors of 1242. The next step is to make pairs of those prime factors. Since 1242 is not a perfect square, the digits of the number can’t be grouped into pairs perfectly.</p>

15 <p>Therefore, calculating √1242 using prime factorization is not straightforward.</p>

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18 <h2>Square Root of 1242 by Long Division Method</h2>

17 <h2>Square Root of 1242 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 check for the closest perfect square 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 check for the closest perfect square 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 digits of 1242 from right to left. Grouping results in 12 and 42.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the digits of 1242 from right to left. Grouping results in 12 and 42.</p>

21 <p><strong>Step 2:</strong>Now we need to find a number whose square is close to or<a>less than</a>12. The number is 3 because 3 squared is 9. This gives a<a>quotient</a>of 3, and subtracting 9 from 12 leaves a<a>remainder</a>of 3.</p>

20 <p><strong>Step 2:</strong>Now we need to find a number whose square is close to or<a>less than</a>12. The number is 3 because 3 squared is 9. This gives a<a>quotient</a>of 3, and subtracting 9 from 12 leaves a<a>remainder</a>of 3.</p>

22 <p><strong>Step 3:</strong>Bring down 42 to make the new<a>dividend</a>342. Double the current quotient to get the new<a>divisor</a>'s base: 2 × 3 = 6.</p>

21 <p><strong>Step 3:</strong>Bring down 42 to make the new<a>dividend</a>342. Double the current quotient to get the new<a>divisor</a>'s base: 2 × 3 = 6.</p>

23 <p><strong>Step 4:</strong>Find a digit 'n' such that 6n × n ≤ 342. By trial, 65 × 5 = 325, which is less than 342.</p>

22 <p><strong>Step 4:</strong>Find a digit 'n' such that 6n × n ≤ 342. By trial, 65 × 5 = 325, which is less than 342.</p>

24 <p><strong>Step 5:</strong>Subtract 325 from 342, leaving a remainder of 17.</p>

23 <p><strong>Step 5:</strong>Subtract 325 from 342, leaving a remainder of 17.</p>

25 <p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point to the quotient and bring down two zeros to the remainder, making it 1700.</p>

24 <p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point to the quotient and bring down two zeros to the remainder, making it 1700.</p>

26 <p><strong>Step 7:</strong>The new divisor base is 70 (from 65), and find a digit 'n' such that 70n × n ≤ 1700.</p>

25 <p><strong>Step 7:</strong>The new divisor base is 70 (from 65), and find a digit 'n' such that 70n × n ≤ 1700.</p>

27 <p><strong>Step 8:</strong>Continue this process to get more decimal places.</p>

26 <p><strong>Step 8:</strong>Continue this process to get more decimal places.</p>

28 <p>So, the square root of √1242 is approximately 35.229.</p>

27 <p>So, the square root of √1242 is approximately 35.229.</p>

29 <h2>Square Root of 1242 by Approximation Method</h2>

28 <h2>Square Root of 1242 by Approximation Method</h2>

30 <p>The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let's learn how to find the square root of 1242 using the approximation method.</p>

29 <p>The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let's learn how to find the square root of 1242 using the approximation method.</p>

31 <p><strong>Step 1:</strong>Identify the closest perfect squares around 1242. The closest perfect squares are 1225 (35^2) and 1296 (36^2). Thus, √1242 falls between 35 and 36.</p>

30 <p><strong>Step 1:</strong>Identify the closest perfect squares around 1242. The closest perfect squares are 1225 (35^2) and 1296 (36^2). Thus, √1242 falls between 35 and 36.</p>

32 <p><strong>Step 2:</strong>Use the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Using the formula: (1242 - 1225) / (1296 - 1225) = 17 / 71 ≈ 0.239 Adding this to 35, the approximate square root of 1242 is 35 + 0.239 = 35.239</p>

31 <p><strong>Step 2:</strong>Use the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Using the formula: (1242 - 1225) / (1296 - 1225) = 17 / 71 ≈ 0.239 Adding this to 35, the approximate square root of 1242 is 35 + 0.239 = 35.239</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1242</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1242</h2>

34 <p>Students can make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.</p>

33 <p>Students can make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.</p>

34 + <h2>Download Worksheets</h2>

35 <h3>Problem 1</h3>

36 <p>Can you help Max find the area of a square box if its side length is √1242?</p>

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

38 <p>The area of the square is approximately 1541.16 square units.</p>

39 <h3>Explanation</h3>

40 <p>The area of a square = side².</p>

41 <p>The side length is given as √1242.</p>

42 <p>Area of the square = side² = √1242 × √1242 = 35.229 × 35.229 ≈ 1242</p>

43 <p>Therefore, the area of the square box is approximately 1242 square units.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

46 <p>A square-shaped building measuring 1242 square feet is built; if each of the sides is √1242, what will be the square feet of half of the building?</p>

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

48 <p>621 square feet</p>

49 <h3>Explanation</h3>

50 <p>Since the building is square-shaped, dividing the total area by 2 gives half the area.</p>

51 <p>Dividing 1242 by 2 gives 621.</p>

52 <p>So half of the building measures 621 square feet.</p>

53 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

55 <p>Calculate √1242 × 5.</p>

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

57 <p>176.145</p>

58 <h3>Explanation</h3>

59 <p>The first step is to find the square root of 1242, which is approximately 35.229.</p>

60 <p>Then multiply 35.229 by 5.</p>

61 <p>So, 35.229 × 5 ≈ 176.145</p>

62 <p>Well explained 👍</p>

63 <h3>Problem 4</h3>

64 <p>What will be the square root of (1236 + 6)?</p>

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

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

67 <h3>Explanation</h3>

68 <p>To find the square root, we first find the sum of (1236 + 6), which equals 1242.</p>

69 <p>The square root of 1242 is approximately 35.229.</p>

70 <p>Well explained 👍</p>

71 <h3>Problem 5</h3>

72 <p>Find the perimeter of the rectangle if its length ‘l’ is √1242 units and the width ‘w’ is 38 units.</p>

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

74 <p>The perimeter of the rectangle is approximately 146.458 units.</p>

75 <h3>Explanation</h3>

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

77 <p>Perimeter = 2 × (√1242 + 38)</p>

78 <p>= 2 × (35.229 + 38)</p>

79 <p>≈ 2 × 73.229</p>

80 <p>≈ 146.458 units.</p>

81 <p>Well explained 👍</p>

82 <h2>FAQ on Square Root of 1242</h2>

83 <h3>1.What is √1242 in its simplest form?</h3>

84 <p>The prime factorization of 1242 is 2 × 3 × 3 × 3 × 23, so the simplest form of √1242 is √(2 × 3^3 × 23).</p>

85 <h3>2.Mention the factors of 1242.</h3>

86 <p>Factors of 1242 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414, 621, and 1242.</p>

87 <h3>3.Calculate the square of 1242.</h3>

88 <p>We get the square of 1242 by multiplying the number by itself, that is, 1242 × 1242 = 1,542,564.</p>

89 <h3>4.Is 1242 a prime number?</h3>

90 <p>1242 is not a<a>prime number</a>, as it has more than two factors.</p>

91 <h3>5.1242 is divisible by?</h3>

92 <p>1242 is divisible by 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414, 621, and 1242.</p>

93 <h2>Important Glossaries for the Square Root of 1242</h2>

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

95 <li><strong>Irrational number:</strong>An irrational number cannot be written in the form of p/q, where q is not equal to zero and p and q are integers. </li>

96 <li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 36 is a perfect square because it can be written as 6^2. </li>

97 <li><strong>Prime factorization:</strong>The process of expressing a number as the product of its prime factors. </li>

98 <li><strong>Decimal:</strong>A number that includes a whole number and a fractional part, represented with a decimal point, such as 7.86, 8.65, and 9.42.</li>

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

100 <p>▶</p>

101 <h2>Jaskaran Singh Saluja</h2>

102 <h3>About the Author</h3>

103 <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>

104 <h3>Fun Fact</h3>

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