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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 like vehicle design, finance, etc. Here, we will discuss the square root of 70.</p>

4 <h2>What is the Square Root of 70?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 70 is not a<a>perfect square</a>. The square root of 70 is expressed in both radical and<a>exponential form</a>.</p>

6 <p>In the radical form, it is expressed as √70, whereas (70)(1/2) is in exponential form. √70 ≈ 8.3666, 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 70</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>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 70 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 70 is broken down into its prime factors.</p>

14 <p><strong>Step 1:</strong>Finding the prime factors of 70 Breaking it down, we get 2 x 5 x 7.</p>

15 <p><strong>Step 2:</strong>Now we found out the prime factors of 70. The second step is to make pairs of those prime factors. Since 70 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>

16 <p>Therefore, calculating √70 using prime factorization is impossible.</p>

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19 <h2>Square Root of 70 by Long Division Method</h2>

18 <h2>Square Root of 70 by Long Division Method</h2>

20 <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>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>

21 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 70, we need to group it as 70.</p>

20 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 70, we need to group it as 70.</p>

22 <p><strong>Step 2:</strong>Now we need to find n whose square is closest to 70. We can say n as 8 because 8 x 8 = 64, which is lesser than 70. Now the<a>quotient</a>is 8 after subtracting 70 - 64, the<a>remainder</a>is 6.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is closest to 70. We can say n as 8 because 8 x 8 = 64, which is lesser than 70. Now the<a>quotient</a>is 8 after subtracting 70 - 64, the<a>remainder</a>is 6.</p>

23 <p><strong>Step 3:</strong>Since the<a>dividend</a>is<a>less than</a>the<a>divisor</a>, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the remainder. Now the new remainder is 600.</p>

22 <p><strong>Step 3:</strong>Since the<a>dividend</a>is<a>less than</a>the<a>divisor</a>, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the remainder. Now the new remainder is 600.</p>

24 <p><strong>Step 4:</strong>Double the quotient and consider it as the new divisor. The new divisor will be 8 x 2 = 16. We need to find a digit n such that 16n x n ≤ 600. Let us consider n as 3. Then 163 x 3 = 489.</p>

23 <p><strong>Step 4:</strong>Double the quotient and consider it as the new divisor. The new divisor will be 8 x 2 = 16. We need to find a digit n such that 16n x n ≤ 600. Let us consider n as 3. Then 163 x 3 = 489.</p>

25 <p><strong>Step 5:</strong>Subtract 600 from 489, the difference is 111, and the quotient becomes 8.3</p>

24 <p><strong>Step 5:</strong>Subtract 600 from 489, the difference is 111, and the quotient becomes 8.3</p>

26 <p><strong>Step 6:</strong>Continue doing these steps until we get the desired decimal places. Suppose if there are no decimal values, continue till the remainder is zero.</p>

25 <p><strong>Step 6:</strong>Continue doing these steps until we get the desired decimal places. Suppose if there are no decimal values, continue till the remainder is zero.</p>

27 <p>So the square root of √70 ≈ 8.3666.</p>

26 <p>So the square root of √70 ≈ 8.3666.</p>

28 <h2>Square Root of 70 by Approximation Method</h2>

27 <h2>Square Root of 70 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 70 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 70 using the approximation method.</p>

30 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares around 70. The smallest perfect square less than 70 is 64, and the largest perfect square<a>greater than</a>70 is 81. √70 falls somewhere between 8 and 9.</p>

29 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares around 70. The smallest perfect square less than 70 is 64, and the largest perfect square<a>greater than</a>70 is 81. √70 falls somewhere between 8 and 9.</p>

31 <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>

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>

32 <p>Using the formula, (70 - 64) ÷ (81 - 64) = 6 ÷ 17 ≈ 0.3529.</p>

31 <p>Using the formula, (70 - 64) ÷ (81 - 64) = 6 ÷ 17 ≈ 0.3529.</p>

33 <p>Adding this to the smaller perfect square root gives 8 + 0.3529 ≈ 8.3529.</p>

32 <p>Adding this to the smaller perfect square root gives 8 + 0.3529 ≈ 8.3529.</p>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 70</h2>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 70</h2>

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

34 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make 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 √50?</p>

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

39 <p>The area of the square is approximately 50 square units.</p>

40 <h3>Explanation</h3>

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

42 <p>The side length is given as √50.</p>

43 <p>Area of the square = side² = √50 x √50 = 50.</p>

44 <p>Therefore, the area of the square box is approximately 50 square units.</p>

45 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

47 <p>A square-shaped field measuring 70 square feet is built; if each of the sides is √70, what will be the square feet of half of the field?</p>

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

49 <p>35 square feet</p>

50 <h3>Explanation</h3>

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

52 <p>Dividing 70 by 2, we get 35. So half of the field measures 35 square feet.</p>

53 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

55 <p>Calculate √70 x 4.</p>

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

57 <p>Approximately 33.4664</p>

58 <h3>Explanation</h3>

59 <p>The first step is to find the square root of 70, which is approximately 8.3666.</p>

60 <p>The second step is to multiply 8.3666 with 4. So 8.3666 x 4 ≈ 33.4664.</p>

61 <p>Well explained 👍</p>

62 <h3>Problem 4</h3>

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

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

65 <p>The square root is 8.3666</p>

66 <h3>Explanation</h3>

67 <p>To find the square root, we need to find the sum of (64 + 6). 64 + 6 = 70, and then √70 ≈ 8.3666.</p>

68 <p>Therefore, the square root of (64 + 6) is approximately 8.3666.</p>

69 <p>Well explained 👍</p>

70 <h3>Problem 5</h3>

71 <p>Find the perimeter of the rectangle if its length ‘l’ is √70 units and the width ‘w’ is 30 units.</p>

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

73 <p>We find the perimeter of the rectangle as approximately 76.7332 units.</p>

74 <h3>Explanation</h3>

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

76 <p>Perimeter = 2 × (√70 + 30)</p>

77 <p>= 2 × (8.3666 + 30) ≈ 2 × 38.3666</p>

78 <p>= 76.7332 units.</p>

79 <p>Well explained 👍</p>

80 <h2>FAQ on Square Root of 70</h2>

81 <h3>1.What is √70 in its simplest form?</h3>

82 <p>The prime factorization of 70 is 2 x 5 x 7, so the simplest form of √70 is √(2 x 5 x 7).</p>

83 <h3>2.Mention the factors of 70.</h3>

84 <p>Factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.</p>

85 <h3>3.Calculate the square of 70.</h3>

86 <p>We get the square of 70 by multiplying the number by itself, that is 70 x 70 = 4900.</p>

87 <h3>4.Is 70 a prime number?</h3>

88 <h3>5.70 is divisible by?</h3>

89 <p>70 has several factors; those are 1, 2, 5, 7, 10, 14, 35, and 70.</p>

90 <h2>Important Glossaries for the Square Root of 70</h2>

91 <ul><li><strong>Square root:</strong>A square root is the number that gives the original number when multiplied by itself. For example, 42 = 16, and the inverse of the square is the square root, so √16 = 4.</li>

92 </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>

93 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the positive square root is more commonly used in real-world scenarios. This is known as the principal square root.</li>

94 </ul><ul><li><strong>Prime factorization:</strong>It is the process of expressing a number as the product of its prime factors. For example, the prime factorization of 70 is 2, 5, and 7.</li>

95 </ul><ul><li><strong>Long division method:</strong>A mathematical method used to find the square root of non-perfect squares by calculating each digit of the square root one at a time.</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>