Rivalry2

HTML Diff

2 added 2 removed

Original 2026-01-01

Modified 2026-02-28

1 - <p>325 Learners</p>

1 + <p>352 Learners</p>

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 71.</p>

4 <h2>What is the Square Root of 71?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 71 is not a<a>perfect square</a>. The square root of 71 is expressed in both radical and<a>exponential form</a>.</p>

6 <p>In the radical form, it is expressed as √71, whereas (71)(1/2) is the exponential form. √71 ≈ 8.42615, 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 71</h2>

8 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>

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

10 <li>Long division method</li>

11 <li>Approximation method</li>

12 </ol><h2>Square Root of 71 by Prime Factorization Method</h2>

13 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 71 is broken down into its prime factors. 71 is a<a>prime number</a>, so it cannot be broken down into smaller prime factors.</p>

14 <p>Therefore, calculating √71 using prime factorization is not feasible.</p>

15 <h3>Explore Our Programs</h3>

16 - <p>No Courses Available</p>

17 <h2>Square Root of 71 by Long Division Method</h2>

16 <h2>Square Root of 71 by Long Division Method</h2>

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>

17 <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>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 71, we need to group it as 71.</p>

18 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 71, we need to group it as 71.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is closest to 71 but<a>less than</a>or equal to 71. We can say n is ‘8’ because 8 × 8 = 64, which is less than 71. Now the<a>quotient</a>is 8, and after subtracting 64 from 71, the<a>remainder</a>is 7.</p>

19 <p><strong>Step 2:</strong>Now we need to find n whose square is closest to 71 but<a>less than</a>or equal to 71. We can say n is ‘8’ because 8 × 8 = 64, which is less than 71. Now the<a>quotient</a>is 8, and after subtracting 64 from 71, the<a>remainder</a>is 7.</p>

21 <p><strong>Step 3:</strong>Since the remainder is not zero, we need to add a<a>decimal</a>point to the quotient and bring down two zeroes to the remainder, making it 700.</p>

20 <p><strong>Step 3:</strong>Since the remainder is not zero, we need to add a<a>decimal</a>point to the quotient and bring down two zeroes to the remainder, making it 700.</p>

22 <p><strong>Step 4:</strong>The new<a>divisor</a>will be the sum of the previous divisor multiplied by 2, i.e., 16, plus a new digit x such that 16x × x is less than or equal to 700. We find that x = 4 works because 164 × 4 = 656.</p>

21 <p><strong>Step 4:</strong>The new<a>divisor</a>will be the sum of the previous divisor multiplied by 2, i.e., 16, plus a new digit x such that 16x × x is less than or equal to 700. We find that x = 4 works because 164 × 4 = 656.</p>

23 <p><strong>Step 5:</strong>Subtract 656 from 700, leaving a remainder of 44.</p>

22 <p><strong>Step 5:</strong>Subtract 656 from 700, leaving a remainder of 44.</p>

24 <p><strong>Step 6:</strong>Repeat the process by adding two more zeroes to make it 4400 and find a new divisor. Continue this process to get more decimal places. The square root of 71 is approximately 8.426.</p>

23 <p><strong>Step 6:</strong>Repeat the process by adding two more zeroes to make it 4400 and find a new divisor. Continue this process to get more decimal places. The square root of 71 is approximately 8.426.</p>

25 <h2>Square Root of 71 by Approximation Method</h2>

24 <h2>Square Root of 71 by Approximation Method</h2>

26 <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 71 using the approximation method.</p>

25 <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 71 using the approximation method.</p>

27 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √71. The smallest perfect square less than 71 is 64, and the largest perfect square<a>greater than</a>71 is 81. √71 falls somewhere between 8 and 9.</p>

26 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √71. The smallest perfect square less than 71 is 64, and the largest perfect square<a>greater than</a>71 is 81. √71 falls somewhere between 8 and 9.</p>

28 <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>

27 <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>Applying the formula: (71 - 64) / (81 - 64) = 7 / 17 ≈ 0.412. Using the formula, we identified the decimal point of our square root.</p>

28 <p>Applying the formula: (71 - 64) / (81 - 64) = 7 / 17 ≈ 0.412. Using the formula, we identified the decimal point of our square root.</p>

30 <p>The next step is adding the value we got initially to the decimal number: 8 + 0.412 ≈ 8.426, so the square root of 71 is approximately 8.426.</p>

29 <p>The next step is adding the value we got initially to the decimal number: 8 + 0.412 ≈ 8.426, so the square root of 71 is approximately 8.426.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 71</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 71</h2>

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

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

32 + <h2>Download Worksheets</h2>

33 <h3>Problem 1</h3>

34 <p>Can you help Max find the area of a square box if its side length is given as √71?</p>

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

36 <p>The area of the square is approximately 71 square units.</p>

37 <h3>Explanation</h3>

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

39 <p>The side length is given as √71.</p>

40 <p>Area of the square = side² = √71 × √71 = 71.</p>

41 <p>Therefore, the area of the square box is approximately 71 square units.</p>

42 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

44 <p>A square-shaped building measuring 71 square feet is built. If each of the sides is √71, what will be the square feet of half of the building?</p>

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

46 <p>35.5 square feet</p>

47 <h3>Explanation</h3>

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

49 <p>Dividing 71 by 2 = 35.5.</p>

50 <p>So half of the building measures 35.5 square feet.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

53 <p>Calculate √71 × 5.</p>

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

55 <p>Approximately 42.13</p>

56 <h3>Explanation</h3>

57 <p>The first step is to find the square root of 71, which is approximately 8.426.</p>

58 <p>The second step is to multiply 8.426 with 5. So 8.426 × 5 ≈ 42.13.</p>

59 <p>Well explained 👍</p>

60 <h3>Problem 4</h3>

61 <p>What will be the square root of (71 + 8)?</p>

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

63 <p>The square root is 9.</p>

64 <h3>Explanation</h3>

65 <p>To find the square root, we need to find the sum of (71 + 8). 71 + 8 = 79, and then √79 ≈ 8.888.</p>

66 <p>Therefore, the square root of (71 + 8) is approximately 8.888.</p>

67 <p>Well explained 👍</p>

68 <h3>Problem 5</h3>

69 <p>Find the perimeter of a rectangle if its length ‘l’ is √71 units and the width ‘w’ is 20 units.</p>

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

71 <p>The perimeter of the rectangle is approximately 56.85 units.</p>

72 <h3>Explanation</h3>

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

74 <p>Perimeter = 2 × (√71 + 20)</p>

75 <p>= 2 × (8.426 + 20)</p>

76 <p>= 2 × 28.426 ≈ 56.85 units.</p>

77 <p>Well explained 👍</p>

78 <h2>FAQ on Square Root of 71</h2>

79 <h3>1.What is √71 in its simplest form?</h3>

80 <p>Since 71 is a prime number, the simplest form of √71 is just √71.</p>

81 <h3>2.Is 71 a prime number?</h3>

82 <p>Yes, 71 is a prime number because it has no divisors other than 1 and itself.</p>

83 <h3>3.Calculate the square of 71.</h3>

84 <p>We get the square of 71 by multiplying the number by itself, that is 71 × 71 = 5041.</p>

85 <h3>4.Is the square root of 71 rational or irrational?</h3>

86 <p>The square root of 71 is irrational because it cannot be expressed as a simple<a>fraction</a>.</p>

87 <h3>5.What are the factors of 71?</h3>

88 <p>The factors of 71 are 1 and 71, as it is a prime number.</p>

89 <h2>Important Glossaries for the Square Root of 71</h2>

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

91 </ul><ul><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 </ul><ul><li><strong>Prime number:</strong>A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. Example: 71 is a prime number.</li>

93 </ul><ul><li><strong>Long division method:</strong>A method used to find more accurate values of square roots of numbers that are not perfect squares by performing long division.</li>

94 </ul><ul><li><strong>Approximation method:</strong>A method used to estimate the square root of a number by finding the nearest perfect squares and calculating the difference.</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>