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1 - <p>1012 Learners</p>

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2 <p>Last updated on<strong>October 30, 2025</strong></p>

3 <p>The square root of 8 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 8. The number 8 has a unique non-negative square root, known as the principal square root.</p>

4 <h2>What Is the Square Root of 8?</h2>

5 <p>The<a>square</a>root of 8 is ±2.82842712475, where 2.82842712475 is the positive solution of the<a>equation</a>x2 = 8. Finding the square root is just the inverse way of squaring a<a>number</a>, and hence, squaring 2.82842712475 will result in 8.</p>

6 <p>The square root of 8 is written as √8 in radical form, where the ‘√’ sign is called the “radical” sign. In<a>exponential form</a>, it is written as (8)1/2.</p>

7 <h3>Square Root of 8 By Prime Factorization</h3>

8 <p>The<a>prime factorization</a>of 8 can be found by dividing the 8 by<a>prime numbers</a>and continuing to divide the quotients until they can’t be divided anymore. After factorizing 8, make pairs out of the<a>factors</a>to get the<a>square root</a>. If there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the acquired pairs.</p>

9 <p>So, Prime factorization of 8 = 2 × 2 × 2 = 2³</p>

10 <p>But here, only a pair of factor 2 can be obtained and a single 2 is remaining</p>

11 <p>So, it can be written as √8 = 2√2.</p>

12 <p>Square root of 8 = √[2 × 2 × 2] = 2√2, i.e., 2.82842712475</p>

13 <h3>Square Root of 8 By Long Division</h3>

14 <p>This is a method, mainly used for obtaining the square root for non-<a>perfect squares</a>. It usually involves the<a>division</a>of the<a>dividend</a>by the<a>divisor</a>, getting a<a>quotient</a>and a<a>remainder</a>too, where the dividend is the number we are finding the square root of.</p>

15 <p>Follow the steps to calculate the square root of 8:</p>

16 <p><strong> Step 1:</strong>Place the number 8, just the same as the image, starting from right to left, and draw a bar above the pair of digits since 8 is a 1-digit number, so simply just draw a bar above 8. </p>

17 <p><strong>Step 2:</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 8. Here, it is 2, because 22=4 < 8</p>

18 <p><strong>Step 3:</strong>Now divide 8 by 2 (the number we got from step 2) and we get a remainder. Double the divisor 2, we get 4 and find the largest possible number A, put it in the right of 4, through this, a double-digit is formed. Now multiply this with the same number A. Repeat this process until you reach the remainder of 0.</p>

19 <p><strong>Step 4:</strong>The quotient we got is the square root. In this case, it is 2.828….</p>

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22 <h3>Square Root of 8 By Approximation</h3>

21 <h3>Square Root of 8 By Approximation</h3>

23 <p>Follow the steps below: </p>

22 <p>Follow the steps below: </p>

24 <p><strong>Step 1:</strong>find the square roots of the perfect squares above and below 8</p>

23 <p><strong>Step 1:</strong>find the square roots of the perfect squares above and below 8</p>

25 <p>Below : 4 → square root of 4 =2 …. (i)</p>

24 <p>Below : 4 → square root of 4 =2 …. (i)</p>

26 <p>Above : 9 →square root of 9 = 3 …..(ii)</p>

25 <p>Above : 9 →square root of 9 = 3 …..(ii)</p>

27 <p><strong>Step 2:</strong>Dividing 8 with one of 2 or 3 </p>

26 <p><strong>Step 2:</strong>Dividing 8 with one of 2 or 3 </p>

28 <p>If we choose 3 and divide 8 by 3, we are getting 2.666 …..(iii)</p>

27 <p>If we choose 3 and divide 8 by 3, we are getting 2.666 …..(iii)</p>

29 <p><strong>Step 3:</strong> find the<a>average</a>of 3 (from step (ii)) and 2.666 (from step (iii))</p>

28 <p><strong>Step 3:</strong> find the<a>average</a>of 3 (from step (ii)) and 2.666 (from step (iii))</p>

30 <p>(3+2.666)/2 = 2.8333 </p>

29 <p>(3+2.666)/2 = 2.8333 </p>

31 <p>Hence, 2.8333 is the approximate square root of 8</p>

30 <p>Hence, 2.8333 is the approximate square root of 8</p>

32 <p>Similarly, try applin these methods on<a>square root of 100</a>and practice.</p>

31 <p>Similarly, try applin these methods on<a>square root of 100</a>and practice.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 8</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 8</h2>

34 <p>When we find the square root of 8, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.</p>

33 <p>When we find the square root of 8, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.</p>

34 + <h2>Download Worksheets</h2>

35 <h3>Problem 1</h3>

36 <p>Estimate the value of √8 using an initial guess of 2.5</p>

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

38 <p>By using the formula,</p>

39 <p>New Guess=(Initial Guess + (Given Number / Initial Guess))/ 2</p>

40 <p>applying the formula, </p>

41 <p>New guess= (2.5 + (8/2.5))/2 </p>

42 <p> = (2.5+ 3.2)/2</p>

43 <p> =5.7/2</p>

44 <p> =2.85</p>

45 <p>Again, repeating the process,</p>

46 <p>New guess= (2.85 + (8/2.85))/2 </p>

47 <p> = (2.85+ 2.807)/2</p>

48 <p> =5.657/2</p>

49 <p> =2.825</p>

50 <p>hence, after a few iterations, the value of √8 is approximately 2.825</p>

51 <p>Answer: 2.825 approx. </p>

52 <h3>Explanation</h3>

53 <p>Using the formula for New Guess, we found the approximate value of the square root 8 by repeated iterations, where New Guess=(Initial Guess + (Given Number / Initial Guess))/ 2 </p>

54 <p>Well explained 👍</p>

55 <h3>Problem 2</h3>

56 <p>Find the length of a side of a square whose area is 8 cm².</p>

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

58 <p> Given, the area = 8 cm2</p>

59 <p>We know that, (side of a square)2 = area of square</p>

60 <p> Or, (side of a square)2 = 8</p>

61 <p>Or, (side of a square)= √8</p>

62 <p>Or, side of a square = ± 2√2.</p>

63 <p>But, the length of a square is a positive quantity only, so, the length of the side is 2√2 cm.</p>

64 <p>Answer: 2√2 cm</p>

65 <h3>Explanation</h3>

66 <p>We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because the square root is the measure of the side of the square.</p>

67 <p>Well explained 👍</p>

68 <h3>Problem 3</h3>

69 <p>Simplify (√8 + √8) ⤫ √8</p>

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

71 <p> (√8 + √8) ⤫ √8 = (2√2 + 2√2) ⤫ 2√2 = 4√2 ⤫ 2√2 = 8 ⤫ 2 =16 </p>

72 <p>Answer: 16</p>

73 <h3>Explanation</h3>

74 <p>We first solved the part inside the brackets, i.e., √8 + √8, which resulted into 4√2, and then multiplying it with √8 which is 2√2, we get 16.</p>

75 <p>Well explained 👍</p>

76 <h3>Problem 4</h3>

77 <p>If x= √8, what is x² -3?</p>

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

79 <p>x= √8</p>

80 <p>⇒ x2 = 8</p>

81 <p>⇒ x2-3 = 8-3</p>

82 <p>⇒ x2-3 = 5</p>

83 <p>Answer: 5</p>

84 <h3>Explanation</h3>

85 <p>We did the square of the given value of x and then subtracted 3 from it.</p>

86 <p>Well explained 👍</p>

87 <h3>Problem 5</h3>

88 <p>If y=√8, find y²</p>

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

90 <p>Firstly, y=√8= 2.8284,</p>

91 <p>Now, squaring y, we get, y2= (2.8284)2=8, or, y2=8</p>

92 <p>Answer: 8</p>

93 <h3>Explanation</h3>

94 <p>Squaring “y” which is the same as squaring the value of √8 resulted as 8.</p>

95 <p>Well explained 👍</p>

96 <h2>FAQs on Square Root 8</h2>

97 <h3>1.Can the value of √8 be negative?</h3>

98 <p>Yes, the square root of 8 can be negative. Rather, it can be both positive and negative. So, (-2<em>√2</em>)² = 8 and (2<em>√2</em>)²= 8, both yield the same result.</p>

99 <h3>2.Is the square root of 8 a whole number?</h3>

100 <h3>3.Is 8 a perfect square or a non-perfect square?</h3>

101 <p>8 is a non-perfect square, since 8 =(2<em>√2</em>) ².</p>

102 <h3>4.Is the square root of 8 a rational or irrational number?</h3>

103 <p>The square root of 8 is ±2<em>√2</em>. So, 2<em>√2</em>is an<a>irrational number</a>since it cannot be obtained by dividing two<a>integers</a>and cannot be written in the form p/q.</p>

104 <h3>5.What is the principal square root of 8?</h3>

105 <p>The principal square root of 8 is ±2<em>√2</em>, which is the positive value, whereas -2<em>√2</em>is not.</p>

106 <h2>Important Glossaries for Square Root of 8</h2>

107 <ul><li><strong>Exponential form</strong>: An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent.</li>

108 </ul><ul><li><strong>Factorization: </strong>Expressing the given expression as a product of its factors</li>

109 </ul><ul><li><strong>Prime Numbers: </strong>Numbers that are greater than 1, having only 2 factors as →1 and Itself. </li>

110 </ul><ul><li> <strong>Rational numbers and Irrational numbers</strong>: The numbers that can be expressed as p/q, where p and q are integers and q is not equal to 0 are called Rational numbers. Numbers that cannot be expressed as p/q, where p and q are integers and q is not equal to 0 are called Irrational numbers. </li>

111 </ul><ul><li><strong>Perfect and non-perfect square numbers</strong>: Perfect square numbers are those numbers whose square roots do not include decimal places. Non-perfect square numbers are those numbers whose square roots comprise decimal places. </li>

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

113 <p>▶</p>

114 <h2>Jaskaran Singh Saluja</h2>

115 <h3>About the Author</h3>

116 <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>

117 <h3>Fun Fact</h3>

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