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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 47.</p>

4 <h2>What is the Square Root of 47?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 47 is not a<a>perfect square</a>. The square root of 47 is expressed in both radical and<a>exponential form</a>.</p>

6 <p>In the radical form, it is expressed as √47, whereas (47)^(1/2) in the exponential form. √47 ≈ 6.85565, 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 <h3>Finding the Square Root of 47</h3>

8 <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: Prime factorization method Long division method Approximation method</p>

9 <h2>Square Root of 47 by Prime Factorization Method</h2>

10 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 47 is broken down into its prime factors:</p>

11 <p><strong>Step 1:</strong>Finding the prime factors of 47 47 is a<a>prime number</a>, so it can only be divided by 1 and 47. Since 47 is not a perfect square, calculating √47 using prime factorization does not provide an exact integer result.</p>

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14 <h2>Square Root of 47 by Long Division Method</h2>

13 <h2>Square Root of 47 by Long Division Method</h2>

15 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we check the closest perfect square numbers 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>

14 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we check the closest perfect square numbers 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>

16 <p><strong>Step 1:</strong>To begin with, group the numbers from right to left. For 47, we consider it as a<a>whole number</a>since it is<a>less than</a>100.</p>

15 <p><strong>Step 1:</strong>To begin with, group the numbers from right to left. For 47, we consider it as a<a>whole number</a>since it is<a>less than</a>100.</p>

17 <p><strong>Step 2:</strong>Find the largest number whose square is less than or equal to 47. We can say n as '6' because 6×6 = 36, which is less than 47. Now the<a>quotient</a>is 6, and after subtracting 36 from 47, the<a>remainder</a>is 11.</p>

16 <p><strong>Step 2:</strong>Find the largest number whose square is less than or equal to 47. We can say n as '6' because 6×6 = 36, which is less than 47. Now the<a>quotient</a>is 6, and after subtracting 36 from 47, the<a>remainder</a>is 11.</p>

18 <p><strong>Step 3:</strong>Bring down a pair of zeroes, making the new<a>dividend</a>1100. Add the old divisor with the same number (6+6) to get 12, which will be our new divisor.</p>

17 <p><strong>Step 3:</strong>Bring down a pair of zeroes, making the new<a>dividend</a>1100. Add the old divisor with the same number (6+6) to get 12, which will be our new divisor.</p>

19 <p><strong>Step 4:</strong>Find 'n' such that 12n × n ≤ 1100. In this case, n is 8, as 128×8 = 1024.</p>

18 <p><strong>Step 4:</strong>Find 'n' such that 12n × n ≤ 1100. In this case, n is 8, as 128×8 = 1024.</p>

20 <p><strong>Step 5:</strong>Subtract 1024 from 1100, resulting in a remainder of 76. The quotient is now 6.8.</p>

19 <p><strong>Step 5:</strong>Subtract 1024 from 1100, resulting in a remainder of 76. The quotient is now 6.8.</p>

21 <p><strong>Step 6:</strong>Continue this process by bringing down more pairs of zeroes and finding the next digit. Following these steps, you continue until you achieve the desired level of accuracy.</p>

20 <p><strong>Step 6:</strong>Continue this process by bringing down more pairs of zeroes and finding the next digit. Following these steps, you continue until you achieve the desired level of accuracy.</p>

22 <p>The square root of 47 is approximately 6.855.</p>

21 <p>The square root of 47 is approximately 6.855.</p>

23 <h2>Square Root of 47 by Approximation Method</h2>

22 <h2>Square Root of 47 by Approximation Method</h2>

24 <p>The approximation method is another method for finding the 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 47 using the approximation method.</p>

23 <p>The approximation method is another method for finding the 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 47 using the approximation method.</p>

25 <p><strong>Step 1:</strong>Find the closest perfect squares of √47. The closest perfect squares are 36 (6²) and 49 (7²). √47 falls somewhere between 6 and 7.</p>

24 <p><strong>Step 1:</strong>Find the closest perfect squares of √47. The closest perfect squares are 36 (6²) and 49 (7²). √47 falls somewhere between 6 and 7.</p>

26 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square)</p>

25 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square)</p>

27 <p>Using the formula (47 - 36) ÷ (49 - 36) = 11/13 ≈ 0.846 Adding this to the smaller root: 6 + 0.846 = 6.846, so the square root of 47 is approximately 6.855.</p>

26 <p>Using the formula (47 - 36) ÷ (49 - 36) = 11/13 ≈ 0.846 Adding this to the smaller root: 6 + 0.846 = 6.846, so the square root of 47 is approximately 6.855.</p>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 47</h2>

27 <h2>Common Mistakes and How to Avoid Them in the Square Root of 47</h2>

29 <p>Students may make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Now let us look at a few common mistakes in detail.</p>

28 <p>Students may make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Now let us look at a few common mistakes in detail.</p>

29 + <h2>Download Worksheets</h2>

30 <h3>Problem 1</h3>

31 <p>Can you help Max find the area of a square box if its side length is given as √47?</p>

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

33 <p>The area of the square is 47 square units.</p>

34 <h3>Explanation</h3>

35 <p>The area of a square is calculated as side².</p>

36 <p>The side length is given as √47.</p>

37 <p>Area of the square = side² = √47 × √47 = 47</p>

38 <p>Therefore, the area of the square box is 47 square units.</p>

39 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

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

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

43 <p>23.5 square feet</p>

44 <h3>Explanation</h3>

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

46 <p>Dividing 47 by 2 gives us 23.5.</p>

47 <p>So half of the building measures 23.5 square feet.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 3</h3>

50 <p>Calculate √47 × 3.</p>

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

52 <p>20.56695</p>

53 <h3>Explanation</h3>

54 <p>The first step is to find the square root of 47, which is approximately 6.855, and then multiply it by 3.</p>

55 <p>So, 6.855 × 3 ≈ 20.56695.</p>

56 <p>Well explained 👍</p>

57 <h3>Problem 4</h3>

58 <p>What will be the square root of (47 + 2)?</p>

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

60 <p>The square root is approximately 7.</p>

61 <h3>Explanation</h3>

62 <p>To find the square root, we need to find the sum of (47 + 2), which equals 49.</p>

63 <p>The square root of 49 is 7.</p>

64 <p>Therefore, the square root of (47 + 2) is ±7.</p>

65 <p>Well explained 👍</p>

66 <h3>Problem 5</h3>

67 <p>Find the perimeter of the rectangle if its length ‘l’ is √47 units and the width ‘w’ is 5 units.</p>

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

69 <p>The perimeter of the rectangle is approximately 23.7113 units.</p>

70 <h3>Explanation</h3>

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

72 <p>Perimeter = 2 × (√47 + 5) = 2 × (6.855 + 5) ≈ 2 × 11.855 = 23.7113 units.</p>

73 <p>Well explained 👍</p>

74 <h2>FAQ on Square Root of 47</h2>

75 <h3>1.What is √47 in its simplest form?</h3>

76 <p>The prime factorization of 47 is just 47 itself as it is a prime number, so the simplest form of √47 is itself, √47.</p>

77 <h3>2.Mention the factors of 47.</h3>

78 <p>Factors of 47 are 1 and 47 since it is a prime number.</p>

79 <h3>3.Calculate the square of 47.</h3>

80 <p>We get the square of 47 by multiplying the number by itself, that is 47 × 47 = 2209.</p>

81 <h3>4.Is 47 a prime number?</h3>

82 <p>Yes, 47 is a prime number as it has only two factors: 1 and 47.</p>

83 <h3>5.47 is divisible by?</h3>

84 <p>47 is only divisible by 1 and 47.</p>

85 <h2>Important Glossaries for the Square Root of 47</h2>

86 <ul><li><strong>Square root:</strong>A square root of a number is one of the two equal factors of the number. For example, 4² = 16, and the inverse operation is the square root, which is √16 = 4. </li>

87 <li><strong>Irrational number:</strong>An irrational number cannot be written as a simple fraction (p/q) where q ≠ 0. For example, √47 is irrational. </li>

88 <li><strong>Prime number:</strong>A prime number is a number greater than 1 with no divisors other than 1 and itself. For example, 47 is a prime number. </li>

89 <li><strong>Decimal approximation:</strong>A method of expressing numbers by using a finite sequence of digits after the decimal point to approximate values like √47 ≈ 6.855. </li>

90 <li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 49 is a perfect square because it is 7².</li>

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

92 <p>▶</p>

93 <h2>Jaskaran Singh Saluja</h2>

94 <h3>About the Author</h3>

95 <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>

96 <h3>Fun Fact</h3>

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