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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 various fields such as vehicle design and finance. Here, we will discuss the square root of 42.</p>

4 <h2>What is the Square Root of 42?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 42 is not a<a>perfect square</a>. The square root of 42 is expressed in both radical and<a>exponential form</a>.</p>

6 <p>In the radical form, it is expressed as √42, whereas (42)^(1/2) in the exponential form. √42 ≈ 6.4807, 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>

7 <h2>Finding the Square Root of 42</h2>

8 <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 long-<a>division</a>and approximation methods are used. Let us now learn the following methods:</p>

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

10 <li>Long division method</li>

11 <li>Approximation method</li>

12 </ul><h3>Square Root of 42 by Prime Factorization Method</h3>

13 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 42 is broken down into its prime factors.</p>

14 <p><strong>Step 1:</strong>Finding the prime factors of 42 Breaking it down, we get 2 x 3 x 7.</p>

15 <p><strong>Step 2:</strong>Now we found the prime factors of 42. The second step is to make pairs of those prime factors. Since 42 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 42 using prime factorization is not exact.</p>

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18 <h2>Square Root of 42 by Long Division Method</h2>

17 <h2>Square Root of 42 by Long Division Method</h2>

19 <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>

18 <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>

20 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 42, it is already a two-digit number, so we can consider it as 42.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 42, it is already a two-digit number, so we can consider it as 42.</p>

21 <p><strong>Step 2:</strong>Now we need to find a number whose square is<a>less than</a>or equal to 42. We can say n as '6' because 6 x 6 = 36, which is less than 42. Now, the<a>quotient</a>is 6, and after subtracting 36 from 42, the<a>remainder</a>is 6.</p>

20 <p><strong>Step 2:</strong>Now we need to find a number whose square is<a>less than</a>or equal to 42. We can say n as '6' because 6 x 6 = 36, which is less than 42. Now, the<a>quotient</a>is 6, and after subtracting 36 from 42, the<a>remainder</a>is 6.</p>

22 <p><strong>Step 3:</strong>Add a<a>decimal</a>point to the quotient and bring down two zeros, making the new<a>dividend</a>600.</p>

21 <p><strong>Step 3:</strong>Add a<a>decimal</a>point to the quotient and bring down two zeros, making the new<a>dividend</a>600.</p>

23 <p><strong>Step 4:</strong>Double the current quotient to get 12, which will be part of our new divisor.</p>

22 <p><strong>Step 4:</strong>Double the current quotient to get 12, which will be part of our new divisor.</p>

24 <p><strong>Step 5:</strong>Find a digit, let's say m, such that 12m x m is less than or equal to 600. Here, m is 4, since 124 x 4 = 496.</p>

23 <p><strong>Step 5:</strong>Find a digit, let's say m, such that 12m x m is less than or equal to 600. Here, m is 4, since 124 x 4 = 496.</p>

25 <p><strong>Step 6:</strong>Subtract 496 from 600, the difference is 104, and the quotient is 6.4.</p>

24 <p><strong>Step 6:</strong>Subtract 496 from 600, the difference is 104, and the quotient is 6.4.</p>

26 <p><strong>Step 7:</strong>Continue this process to find more decimal places if needed.</p>

25 <p><strong>Step 7:</strong>Continue this process to find more decimal places if needed.</p>

27 <p>So, the square root of √42 is approximately 6.48.</p>

26 <p>So, the square root of √42 is approximately 6.48.</p>

28 <h2>Square Root of 42 by Approximation Method</h2>

27 <h2>Square Root of 42 by Approximation Method</h2>

29 <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 42 using the approximation method.</p>

28 <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 42 using the approximation method.</p>

30 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √42. The smallest perfect square less than 42 is 36 and the largest perfect square<a>greater than</a>42 is 49. √42 falls somewhere between 6 and 7.</p>

29 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √42. The smallest perfect square less than 42 is 36 and the largest perfect square<a>greater than</a>42 is 49. √42 falls somewhere between 6 and 7.</p>

31 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (42 - 36) / (49 - 36) = 6/13 ≈ 0.46</p>

30 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (42 - 36) / (49 - 36) = 6/13 ≈ 0.46</p>

32 <p>Using the formula, we determined the decimal part of our square root. The next step is adding the value we got initially to the decimal number: 6 + 0.46 ≈ 6.46.</p>

31 <p>Using the formula, we determined the decimal part of our square root. The next step is adding the value we got initially to the decimal number: 6 + 0.46 ≈ 6.46.</p>

33 <p>Thus, the square root of 42 is approximately 6.46.</p>

32 <p>Thus, the square root of 42 is approximately 6.46.</p>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 42</h2>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 42</h2>

35 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods like long division. Let's look at a few of these mistakes in detail.</p>

34 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods like long division. Let's look at a few of these 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 √42?</p>

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

39 <p>The area of the square is 42 square units.</p>

40 <h3>Explanation</h3>

41 <p>The area of the square = side^2. The side length is given as √42.</p>

42 <p>Area of the square = side^2 = √42 x √42 = 42.</p>

43 <p>Therefore, the area of the square box is 42 square units.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

46 <p>A square-shaped building measuring 42 square feet is built; if each of the sides is √42, what will be the square feet of half of the building?</p>

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

48 <p>21 square feet</p>

49 <h3>Explanation</h3>

50 <p>We can divide the given area by 2 since the building is square-shaped.</p>

51 <p>Dividing 42 by 2 = we get 21.</p>

52 <p>So half of the building measures 21 square feet.</p>

53 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

55 <p>Calculate √42 x 5.</p>

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

57 <p>Approximately 32.4</p>

58 <h3>Explanation</h3>

59 <p>The first step is to find the square root of 42, which is approximately 6.48.</p>

60 <p>The second step is to multiply 6.48 by 5.</p>

61 <p>So 6.48 x 5 = approximately 32.4.</p>

62 <p>Well explained 👍</p>

63 <h3>Problem 4</h3>

64 <p>What will be the square root of (36 + 6)?</p>

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

66 <p>The square root is 6.</p>

67 <h3>Explanation</h3>

68 <p>To find the square root, we need to find the sum of (36 + 6). 36 + 6 = 42, and then √42 = approximately 6.48.</p>

69 <p>Therefore, the square root of (36 + 6) is approximately ±6.48.</p>

70 <p>Well explained 👍</p>

71 <h3>Problem 5</h3>

72 <p>Find the perimeter of the rectangle if its length ‘l’ is √42 units and the width ‘w’ is 38 units.</p>

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

74 <p>We find the perimeter of the rectangle is approximately 88.96 units.</p>

75 <h3>Explanation</h3>

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

77 <p>Perimeter = 2 × (√42 + 38) = 2 × (6.48 + 38) = 2 × 44.48 = approximately 88.96 units.</p>

78 <p>Well explained 👍</p>

79 <h2>FAQ on Square Root of 42</h2>

80 <h3>1.What is √42 in its simplest form?</h3>

81 <p>The prime factorization of 42 is 2 x 3 x 7, so the simplest form of √42 is √(2 x 3 x 7).</p>

82 <h3>2.Mention the factors of 42.</h3>

83 <p>Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.</p>

84 <h3>3.Calculate the square of 42.</h3>

85 <p>We get the square of 42 by multiplying the number by itself, that is 42 x 42 = 1764.</p>

86 <h3>4.Is 42 a prime number?</h3>

87 <h3>5.42 is divisible by?</h3>

88 <p>42 has many factors; those are 1, 2, 3, 6, 7, 14, 21, and 42.</p>

89 <h2>Important Glossaries for the Square Root of 42</h2>

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

91 <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>

92 <li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the positive square root is typically used due to its applications in the real world. </li>

93 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example: 36 is a perfect square because it is 6^2. </li>

94 <li><strong>Long division method:</strong>A mathematical procedure used to find the square root of non-perfect square numbers by dividing the number into pairs of digits.</li>

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

96 <p>▶</p>

97 <h2>Jaskaran Singh Saluja</h2>

98 <h3>About the Author</h3>

99 <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>

100 <h3>Fun Fact</h3>

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