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

3 <p>The square root of 100 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 100. The number 100 has a unique non-negative square root, called the principal square root.</p>

4 <h2>What Is the Square Root of 100?</h2>

5 <p>The<a>square</a>root of 100 is ±10, where 10 is the positive solution of the<a>equation</a></p>

6 <p> x2 = 100. Finding the square root is just the inverse of squaring a<a>number</a>and hence, squaring 10 will result in 100. </p>

7 <p>The square root of 100 is written as √100 in radical form, where the ‘√’ sign is called the “radical” sign. In<a>exponential form</a>, it is written as (100)1/2 </p>

8 <h2>Finding the Square Root of 100</h2>

9 <p>We can find the<a>square root</a>of 100 through various methods. They are:</p>

10 <p>i) Prime factorization method</p>

11 <p>ii) Long<a>division</a>method</p>

12 <p>iii) Repeated<a>subtraction</a>method</p>

13 <h3>Square Root of 100 By Prime Factorization Method</h3>

14 <p>The prime factorization of 100 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. After factorizing 100, make pairs out of the<a>factors</a>to get the square root.</p>

15 <p>So, Prime factorization of 100 = 2 × 5 ×2 × 5</p>

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18 <h3>Square Root of 100 By Long Division Method</h3>

17 <h3>Square Root of 100 By Long Division Method</h3>

19 <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>

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>

20 <p>Follow the steps to calculate the square root of 100:</p>

19 <p>Follow the steps to calculate the square root of 100:</p>

21 <p> Step 1: Write the number 100 and draw a bar above the pair of digits from right to left.</p>

20 <p> Step 1: Write the number 100 and draw a bar above the pair of digits from right to left.</p>

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

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

23 <p>Step 3: Now divide 1 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=0 is chosen such that when 0 is written beside the new divisor 2, a 2-digit number is formed →20, and multiplying 0 with 20 gives 0, which is less than or equal to 0. Repeat this process until you reach the remainder of 0. </p>

22 <p>Step 3: Now divide 1 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=0 is chosen such that when 0 is written beside the new divisor 2, a 2-digit number is formed →20, and multiplying 0 with 20 gives 0, which is less than or equal to 0. Repeat this process until you reach the remainder of 0. </p>

24 <p> Step 4: The quotient obtained is the square root of 100. In this case, it is 10.</p>

23 <p> Step 4: The quotient obtained is the square root of 100. In this case, it is 10.</p>

25 <h3>Square Root of 100 By Subtraction Method</h3>

24 <h3>Square Root of 100 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 subtraction 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 a 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 subtraction 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 a count of the number of steps required to obtain 0. Here are the steps:</p>

27 <p>Step 1: take the number 100 and then subtract the first odd number from it. Here, in this case, it is 100-1=99</p>

26 <p>Step 1: take the number 100 and then subtract the first odd number from it. Here, in this case, it is 100-1=99</p>

28 <p>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., 99, and again subtract the next odd number after 1, from 3, i.e., 99-3=96. Like this, we have to proceed further.</p>

27 <p>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., 99, and again subtract the next odd number after 1, from 3, i.e., 99-3=96. Like this, we have to proceed further.</p>

29 <p>Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 10 steps. So, the square root is equal to the count, i.e., the square root of 100 is ±10.</p>

28 <p>Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 10 steps. So, the square root is equal to the count, i.e., the square root of 100 is ±10.</p>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 100</h2>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 100</h2>

31 <p>When we find the square root of 100, 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 100, 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 100π² cm².</p>

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

35 <p> Given, the area of the circle = 100π cm2</p>

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

37 <p> So, </p>

38 <p> πr2 = 100π cm2</p>

39 <p> We get, r2 = 100 cm2</p>

40 <p> r = √100 cm</p>

41 <p> Putting the value of √100 in the above equation, </p>

42 <p> We get, r = ±10 cm</p>

43 <p> Here we will consider the positive value of 10.</p>

44 <p> Therefore, the radius of the circle is 10 cm.</p>

45 <p>Answer: 10cm.</p>

46 <h3>Explanation</h3>

47 <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 10 cm by finding the value of the square root of 100.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 2</h3>

50 <p>Find the length of a side of a square whose area is 100 cm²</p>

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

52 <p> Given, the area = 100 cm2</p>

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

54 <p> Or, (side of a square)2 = 100</p>

55 <p> Or, (side of a square)=<em>√</em>100</p>

56 <p> Or, the side of a square = ± 10.</p>

57 <p> But, the length of a square is a positive quantity only, so, the length of the side is</p>

58 <p> 10 cm.</p>

59 <p>Answer: 10<em></em>cm</p>

60 <h3>Explanation</h3>

61 <p>We know that, (side of a square)2 = area of square. Here, we are given with the l 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>

62 <p>Well explained 👍</p>

63 <h3>Problem 3</h3>

64 <p>Simplify the expression: √100 ╳ √100, √100+√100</p>

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

66 <p> √100 ╳ √100</p>

67 <p> = √(10 ╳ 10) ╳ √(10 ╳ 10)</p>

68 <p> = 10 ╳ 10</p>

69 <p> = 100</p>

70 <p> √100+√100</p>

71 <p> = √(10 ╳ 10) + √(10 ╳ 10) </p>

72 <p> = 10 + 10</p>

73 <p> = 20</p>

74 <p>Answer: 100, 20</p>

75 <h3>Explanation</h3>

76 <p> In the first expression, we multiplied the value of the square root of 100 with itself. In the second expression, we added the value of the square root of 100 with itself.</p>

77 <p>Well explained 👍</p>

78 <h3>Problem 4</h3>

79 <p>If y=√100, find y²</p>

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

81 <p>Firstly, y=√100= 10</p>

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

83 <p> y2=102=100</p>

84 <p> or, y2=100</p>

85 <p>Answer : 100</p>

86 <h3>Explanation</h3>

87 <p>Squaring “y” which is same as squaring the value of √100 resulted to 100.</p>

88 <p>Well explained 👍</p>

89 <h3>Problem 5</h3>

90 <p>Calculate (√100/5 + √100/2)</p>

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

92 <p>√100/5 + √100/2</p>

93 <p> = 10/5 + 10/2</p>

94 <p> = 2 + 5</p>

95 <p> = 7</p>

96 <p> Answer : 7</p>

97 <h3>Explanation</h3>

98 <p>From the given expression, we first found the value of square root of 100 then solved by simple divisions and then simple addition. </p>

99 <p>Well explained 👍</p>

100 <h2>FAQs on 100 Square Root</h2>

101 <h3>1.Is 100 a rational number?</h3>

102 <h3>2.Is 100 a perfect square or a non-perfect square?</h3>

103 <p>100 is a perfect square, since 100 =10 2.</p>

104 <h3>3.Is the square root of 100 a rational or irrational number?</h3>

105 <p>The square root of 100 is ±10. So, 10 is a rational number since it can be obtained by dividing two integers and can be written in the form 10/1. </p>

106 <h3>4.How to write square root of 100?</h3>

107 <p>The square root of 100 is written as √100 in radical form.</p>

108 <h3>5.How is the square root of 100 used in real life?</h3>

109 <p>The square root of 100 can be used in real-life applications, like in<a>geometry</a>, to determine the side length of a square with an area of 100 sq units.</p>

110 <h3>6.How does the square root of 100 compare to the square root of other numbers?</h3>

111 <ul><li> √100 = ±10</li>

112 <li> √25 = ±5</li>

113 <li> √16 =± 4</li>

114 </ul><p>The square root of a perfect square is always an integer</p>

115 <h3>7.What is the square root of 100 in decimal form?</h3>

116 <p> The square root of 100 in<a>decimal</a>form is 10.</p>

117 <h2>Important Glossaries for Square Root of 100</h2>

118 <p>1)Exponential form</p>

119 <p>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.</p>

120 <p>Ex: 2 ⤬ 2 ⤬ 2 ⤬ 2 = 16</p>

121 <p>Or, 2 4 = 16, where 2 is the base, 4 is the exponent </p>

122 <p>2)Factorization </p>

123 <p>Expressing the given expression as a product of its factors</p>

124 <p>Ex: 48=2 ⤬ 2 ⤬ 2 ⤬ 2 ⤬ 3</p>

125 <p>3) Prime Numbers </p>

126 <p>Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....</p>

127 <p>4) Rational numbers and Irrational numbers</p>

128 <p>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. </p>

129 <p>5) perfect and non-perfect square numbers</p>

130 <p>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 </p>

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

132 <p>▶</p>