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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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 59.</p>

4 <h2>What is the Square Root of 59?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 59 is not a<a>perfect square</a>. The square root of 59 is expressed in both radical and exponential forms. In the radical form, it is expressed as √59, whereas (59)^(1/2) in the<a>exponential form</a>. √59 ≈ 7.68115, 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 59</h2>

7 <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 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><h3>Square Root of 59 by Prime Factorization Method</h3>

12 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 59 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 59 59 is a<a>prime number</a>, so it cannot be broken down further.</p>

14 <p><strong>Step 2:</strong>Since 59 is not a perfect square, calculating √59 using prime factorization is not possible.</p>

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17 <h2>Square Root of 59 by Long Division Method</h2>

16 <h2>Square Root of 59 by Long Division Method</h2>

18 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

17 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the number as a pair of two digits from right to left. In the case of 59, it is already a two-digit number.</p>

18 <p><strong>Step 1:</strong>To begin with, we need to group the number as a pair of two digits from right to left. In the case of 59, it is already a two-digit number.</p>

20 <p><strong>Step 2:</strong>We find n whose square is<a>less than</a>or equal to 59. We can say n is '7' because 7 × 7 = 49, which is less than 59. The<a>quotient</a>is 7, and the<a>remainder</a>is 59 - 49 = 10.</p>

19 <p><strong>Step 2:</strong>We find n whose square is<a>less than</a>or equal to 59. We can say n is '7' because 7 × 7 = 49, which is less than 59. The<a>quotient</a>is 7, and the<a>remainder</a>is 59 - 49 = 10.</p>

21 <p><strong>Step 3:</strong>Since the remainder is less than the<a>divisor</a>, add a<a>decimal</a>point and bring down a pair of zeros, making the new dividend 1000.</p>

20 <p><strong>Step 3:</strong>Since the remainder is less than the<a>divisor</a>, add a<a>decimal</a>point and bring down a pair of zeros, making the new dividend 1000.</p>

22 <p><strong>Step 4:</strong>Double the quotient, 7, to get 14. This will be our new divisor's first part.</p>

21 <p><strong>Step 4:</strong>Double the quotient, 7, to get 14. This will be our new divisor's first part.</p>

23 <p><strong>Step 5:</strong>We find a digit 'd' such that 14d × d ≤ 1000. Trying d = 6, we find 146 × 6 = 876.</p>

22 <p><strong>Step 5:</strong>We find a digit 'd' such that 14d × d ≤ 1000. Trying d = 6, we find 146 × 6 = 876.</p>

24 <p><strong>Step 6:</strong>Subtract 876 from 1000 to get a remainder of 124, and the quotient becomes 7.6.</p>

23 <p><strong>Step 6:</strong>Subtract 876 from 1000 to get a remainder of 124, and the quotient becomes 7.6.</p>

25 <p><strong>Step 7:</strong>Continue this process until the desired accuracy is achieved.</p>

24 <p><strong>Step 7:</strong>Continue this process until the desired accuracy is achieved.</p>

26 <p>So, √59 ≈ 7.68</p>

25 <p>So, √59 ≈ 7.68</p>

27 <h2>Square Root of 59 by Approximation Method</h2>

26 <h2>Square Root of 59 by Approximation Method</h2>

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 59 using the approximation method.</p>

27 <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 59 using the approximation method.</p>

29 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares of 59. The smallest perfect square less than 59 is 49, and the largest perfect square<a>greater than</a>59 is 64. Therefore, √59 falls somewhere between 7 and 8.</p>

28 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares of 59. The smallest perfect square less than 59 is 49, and the largest perfect square<a>greater than</a>59 is 64. Therefore, √59 falls somewhere between 7 and 8.</p>

30 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>

29 <p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>

31 <p>Using the formula, (59 - 49) / (64 - 49) = 10 / 15 = 0.6667 Adding this decimal to the smaller integer, we get 7 + 0.67 = 7.67.</p>

30 <p>Using the formula, (59 - 49) / (64 - 49) = 10 / 15 = 0.6667 Adding this decimal to the smaller integer, we get 7 + 0.67 = 7.67.</p>

32 <p>So, the approximate square root of 59 is 7.67.</p>

31 <p>So, the approximate square root of 59 is 7.67.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 59</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 59</h2>

34 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>

33 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in long division methods. Now let us look at a few of those mistakes that students tend to make 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 given as √58?</p>

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

38 <p>The area of the square is approximately 58 square units.</p>

39 <h3>Explanation</h3>

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

41 <p>The side length is given as √58.</p>

42 <p>Area of the square = (√58)² = 58.</p>

43 <p>Therefore, the area of the square box is approximately 58 square units.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

46 <p>A square-shaped building measuring 59 square feet is built; if each of the sides is √59, what will be the square feet of half of the building?</p>

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

48 <p>29.5 square feet</p>

49 <h3>Explanation</h3>

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

51 <p>Dividing 59 by 2 gives us 29.5.</p>

52 <p>So half of the building measures 29.5 square feet.</p>

53 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

55 <p>Calculate √59 × 3.</p>

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

57 <p>Approximately 23.04345</p>

58 <h3>Explanation</h3>

59 <p>The first step is to find the square root of 59, which is approximately 7.68115.</p>

60 <p>The second step is to multiply 7.68115 by 3.</p>

61 <p>So, 7.68115 × 3 ≈ 23.04345.</p>

62 <p>Well explained 👍</p>

63 <h3>Problem 4</h3>

64 <p>What will be the square root of (49 + 10)?</p>

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

66 <p>The square root is 7.81</p>

67 <h3>Explanation</h3>

68 <p>To find the square root, we need to find the sum of (49 + 10). 49 + 10 = 59, and then √59 ≈ 7.68115.</p>

69 <p>Therefore, the square root of (49 + 10) is approximately ±7.68115.</p>

70 <p>Well explained 👍</p>

71 <h3>Problem 5</h3>

72 <p>Find the perimeter of the rectangle if its length ‘l’ is √59 units and the width ‘w’ is 20 units.</p>

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

74 <p>We find the perimeter of the rectangle as approximately 55.36 units.</p>

75 <h3>Explanation</h3>

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

77 <p>Perimeter = 2 × (√59 + 20) = 2 × (7.68115 + 20) ≈ 2 × 27.68115 ≈ 55.36 units.</p>

78 <p>Well explained 👍</p>

79 <h2>FAQ on Square Root of 59</h2>

80 <h3>1.What is √59 in its simplest form?</h3>

81 <p>Since 59 is a prime number, the simplest form of √59 is itself: √59.</p>

82 <h3>2.What are the factors of 59?</h3>

83 <p>Since 59 is a prime number, its only factors are 1 and 59.</p>

84 <h3>3.Calculate the square of 59.</h3>

85 <p>We get the square of 59 by multiplying the number by itself: 59 × 59 = 3481.</p>

86 <h3>4.Is 59 a prime number?</h3>

87 <p>Yes, 59 is a prime number because it has only two factors: 1 and 59.</p>

88 <h3>5.What numbers is 59 divisible by?</h3>

89 <p>59 is only divisible by 1 and 59, as it is a prime number.</p>

90 <h2>Important Glossaries for the Square Root of 59</h2>

91 <ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. Example: 4² = 16, and the square root of 16 is √16 = 4. </li>

92 <li><strong>Irrational number:</strong>An irrational number is a number that cannot be written as a simple fraction (i.e., in the form of p/q where p and q are integers, and q ≠ 0). </li>

93 <li><strong>Prime number:</strong>A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Example: 59. </li>

94 <li><strong>Long division method:</strong>A step-by-step method used to find the square root of a non-perfect square number by repeatedly dividing and averaging. </li>

95 <li><strong>Decimal:</strong>A number that consists of a whole number and fractional part separated by a decimal point, such as 7.68, 8.65, or 9.42.</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>