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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>The square root of 256 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 256. The number 256 has a unique non-negative square root, called the principal square root.</p>

4 <h2>What Is the Square Root of 256?</h2>

5 <p>The<a>square</a>root<a>of</a>256 is ±16, where 16 is the positive solution of the<a>equation</a> x2 = 256. Finding the square root is just the inverse of squaring a<a>number</a>and hence, squaring 16 will result in 256. The square root of 256 is written as √256 in radical form, where the ‘√’ sign is called the “radical” sign. In<a>exponential form</a>, it is written as (256)1/2 </p>

6 <h2>Finding the Square Root of 256</h2>

7 <p>We can find the<a>square root</a>of 256 through various methods. They are:</p>

8 <ul><li>Prime factorization method</li>

9 </ul><ul><li>Long<a>division</a>method</li>

10 </ul><ul><li>Approximation/Estimation method </li>

11 </ul><h3>Square Root of 256 By Prime Factorization Method</h3>

12 <p>The<a>prime factorization</a>of 256 can be found by dividing the number by<a>prime numbers</a>and continuing to divide the quotients until they can’t be separated anymore,<a>i</a>.e., we first prime factorize 256 and then make pairs of two to get the square root.</p>

13 <p>So, Prime factorization of 256 = 2× 2×2×2×2×2×2×2</p>

14 <p>Square root of 256 = √[2× 2×2×2×2×2×2×2] = 2× 2×2×2 =16</p>

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17 <h3>Square Root of 256 By Long Division Method</h3>

16 <h3>Square Root of 256 By Long Division Method</h3>

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

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

19 <p>Follow the steps to calculate the square root of 256:</p>

18 <p>Follow the steps to calculate the square root of 256:</p>

20 <p><strong> Step 1:</strong>Write the number 256 and draw a bar above the pair of digits from right to left.</p>

19 <p><strong> Step 1:</strong>Write the number 256 and draw a bar above the pair of digits from right to left.</p>

21 <p><strong> Step 2:</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 2. Here, it is 1 because 12=1 < 2</p>

20 <p><strong> Step 2:</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 2. Here, it is 1 because 12=1 < 2</p>

22 <p><strong>Step 3:</strong>now divide 256 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder. Double the divisor 1, we get 2, and then the largest possible number A1=6 is chosen such that when 6 is written beside the new divisor 2, a 2-digit number is formed →26, and multiplying 6 with 26 gives 156, which when subtracted from 156, gives 0.</p>

21 <p><strong>Step 3:</strong>now divide 256 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder. Double the divisor 1, we get 2, and then the largest possible number A1=6 is chosen such that when 6 is written beside the new divisor 2, a 2-digit number is formed →26, and multiplying 6 with 26 gives 156, which when subtracted from 156, gives 0.</p>

23 <p>Repeat this process until you reach the remainder of 0.</p>

22 <p>Repeat this process until you reach the remainder of 0.</p>

24 <p> <strong>Step 4:</strong>The quotient obtained is the square root of 256. In this case, it is 16.</p>

23 <p> <strong>Step 4:</strong>The quotient obtained is the square root of 256. In this case, it is 16.</p>

25 <h3>Square Root of 256 By Subtraction Method</h3>

24 <h3>Square Root of 256 By Subtraction Method</h3>

26 <p>We know that the<a>sum</a>of the first n<a>odd numbers</a>is n2. We will use this fact to find square roots through the repeated<a>subtraction</a>method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:</p>

25 <p>We know that the<a>sum</a>of the first n<a>odd numbers</a>is n2. We will use this fact to find square roots through the repeated<a>subtraction</a>method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:</p>

27 <p><strong>Step 1:</strong>Take the number 256 and then subtract the first odd number from it. Here, in this case, it is 256-1=255 Step 2: We have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 255, and again subtract the next odd number after 1, which is 3, → 255-3=252. Like this, we have to proceed further.</p>

26 <p><strong>Step 1:</strong>Take the number 256 and then subtract the first odd number from it. Here, in this case, it is 256-1=255 Step 2: We have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 255, and again subtract the next odd number after 1, which is 3, → 255-3=252. Like this, we have to proceed further.</p>

28 <p><strong>Step 3:</strong>Now we have to count the number of subtraction steps it takes to yield 0 finally.Here, in this case, it takes 16 steps . </p>

27 <p><strong>Step 3:</strong>Now we have to count the number of subtraction steps it takes to yield 0 finally.Here, in this case, it takes 16 steps . </p>

29 <p>So, the square root is equal to the count, i.e., the square root of 256 is ±16.</p>

28 <p>So, the square root is equal to the count, i.e., the square root of 256 is ±16.</p>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 256</h2>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 256</h2>

31 <p>When we find the square root of 256, 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>

30 <p>When we find the square root of 256, 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>

31 + <h2>Download Worksheets</h2>

32 <h3>Problem 1</h3>

33 <p>Find the radius of a circle whose area is 256π cm².</p>

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

35 <p> Given, the area of the circle = 256π cm2</p>

36 <p>Now, area = πr2 (r is the radius of the circle)</p>

37 <p>So, πr2 = 256π cm2</p>

38 <p>We get, r2 = 256 cm2</p>

39 <p>r = √256 cm</p>

40 <p>Putting the value of √256 in the above equation, </p>

41 <p>We get, r = ±16 cm</p>

42 <p>Here we will consider the positive value of 16.</p>

43 <p>Therefore, the radius of the circle is 16 cm</p>

44 <p>. Answer: 16 cm. </p>

45 <h3>Explanation</h3>

46 <p>We know that, area of a circle = πr2 (r is the radius of the circle). According to this equation, we are getting the value of “r” as 16 cm by finding the value of the square root of 256. </p>

47 <p>Well explained 👍</p>

48 <h3>Problem 2</h3>

49 <p>Find the length of a side of a square whose area is 256 cm²</p>

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

51 <p>Given, the area = 256 cm2</p>

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

53 <p>Or, (side of a square)2 = 256</p>

54 <p>Or, (side of a square)= √256</p>

55 <p>Or, the side of a square = ± 16.</p>

56 <p>But, the length of a square is a positive quantity only, so, the length of the side is 16 cm.</p>

57 <p>Answer: 16 cm </p>

58 <h3>Explanation</h3>

59 <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 its square root is the measure of the side of the square </p>

60 <p>Well explained 👍</p>

61 <h3>Problem 3</h3>

62 <p>Simplify the expression: √256 ╳ √256, √256+√256</p>

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

64 <p> √256 ╳ √256</p>

65 <p> = √(16 ╳ 16) ╳ √(16 ╳ 16)</p>

66 <p> = 16 ╳ 16</p>

67 <p> = 256</p>

68 <p>√256+√256</p>

69 <p>= √(16 ╳ 16) + √(16 ╳ 16) </p>

70 <p>= 16 + 16</p>

71 <p>= 32</p>

72 <p>Answer: 256, 32 </p>

73 <h3>Explanation</h3>

74 <p>In the first expression, we multiplied the value of the square root of 256 with itself. In the second expression, we added the value of the square root of 256 with itself. </p>

75 <p>Well explained 👍</p>

76 <h3>Problem 4</h3>

77 <p>If y=√256, find y²</p>

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

79 <p>firstly, y=√256= 16</p>

80 <p>Now, squaring y, we get, </p>

81 <p>y2=162=256</p>

82 <p>or, y2=256</p>

83 <p>Answer : 256 </p>

84 <h3>Explanation</h3>

85 <p>squaring “y” which is same as squaring the value of √256 resulted to 256</p>

86 <p>Well explained 👍</p>

87 <h3>Problem 5</h3>

88 <p>Calculate (√256/4 + √256/8)</p>

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

90 <p>√256/4 + √256/8</p>

91 <p> = 16/4 + 16/8</p>

92 <p> = 4 + 2</p>

93 <p> = 6</p>

94 <p>Answer : 6 </p>

95 <h3>Explanation</h3>

96 <p>From the given expression, we first found the value of square root of 256 then solved by simple divisions and then simple addition. </p>

97 <p>Well explained 👍</p>

98 <h2>FAQs on 256 Square Root</h2>

99 <h3>1.What is the square root of -256?</h3>

100 <h3>2.Is 256 a rational number?</h3>

101 <h3>3.Is 256 a perfect square or a non-perfect square?</h3>

102 <p>256 is a perfect square since 256 =16 2. </p>

103 <h3>4.Is the square root of 256 a rational or irrational number?</h3>

104 <p> The square root of 256 is ±16. So, 16 is a rational number since it can be obtained by dividing two integers and can be written in the form 16/1 </p>

105 <h3>5.What is the principal square root of 256?</h3>

106 <p> The principal square root of 256 is ±16, the positive value, but not -16 </p>

107 <h3>6.LCM of 256?</h3>

108 <h2>Important Glossaries for Square Root of 256</h2>

109 <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. Ex: 2 × 2 × 2 × 2 = 16 Or, 2 4 = 16, where 2 is the base, 4 is the exponent </li>

110 </ul><ul><li><strong>Prime Factorization:</strong> Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3</li>

111 </ul><ul><li><strong>Prime Numbers:</strong>Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....</li>

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

113 </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. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24</li>

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

115 <p>▶</p>

116 <h2>Jaskaran Singh Saluja</h2>

117 <h3>About the Author</h3>

118 <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>

119 <h3>Fun Fact</h3>

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