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1 - <p>420 Learners</p>

1 + <p>462 Learners</p>

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

3 <p>A number which gives the number itself on multiplication by itself is called the ‘square root’. 117 is a non-perfect square, which is a number whose square roots have a decimal or fraction in them. Learning to find the square root of numbers helps us to solve practical problems in geometry, to make financial estimations.</p>

4 <h2>What is the square root of 117?</h2>

5 <p>The approximate value of √117 is 10.816653. In its<a>exponential form</a>, we write it as → (117)½. Let’s now learn more about the<a>square</a>root of 117. </p>

6 <h2>Finding the square root of 117</h2>

7 <p>Children learn different methods to solve square roots. Few methods are well-used and approved. These methods are explained below. </p>

8 <h3>Square root of 117 using the prime factorization method</h3>

9 <p>Here, we break the<a>numbers</a>into their<a>prime factors</a>.</p>

10 <p>Prime factorization of 117; </p>

11 <p>117= 3×3×13 </p>

12 <p>All prime factors cannot be paired and 117 cannot be simplified to a<a>perfect square</a>. Hence, the<a>square root</a>of 117 cannot be expressed in simple radical form. </p>

13 <p>√117= ∛13 </p>

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16 <h3>Square root of 117 using the division method</h3>

15 <h3>Square root of 117 using the division method</h3>

17 <p>For non-perfect squares, we often use the nearest perfect square value to find the value of a square root. Follow the below steps; </p>

16 <p>For non-perfect squares, we often use the nearest perfect square value to find the value of a square root. Follow the below steps; </p>

18 <p><strong>Step 1:</strong>Write the number 117 to perform a<a>long division</a>.</p>

17 <p><strong>Step 1:</strong>Write the number 117 to perform a<a>long division</a>.</p>

19 <p><strong>Step 2:</strong>Find a perfect square number that is<a>less than</a>or equal to 117. For 117, the number is 100 (102). </p>

18 <p><strong>Step 2:</strong>Find a perfect square number that is<a>less than</a>or equal to 117. For 117, the number is 100 (102). </p>

20 <p><strong>Step 3:</strong>Divide 117 by 10. The<a>remainder</a>will be 17 and<a>quotient</a>will be 10.</p>

19 <p><strong>Step 3:</strong>Divide 117 by 10. The<a>remainder</a>will be 17 and<a>quotient</a>will be 10.</p>

21 <p><strong>Step 4:</strong>Bring down the remainder (17) and add two zeros. Add a<a>decimal</a>point to the quotient, it becomes 10.0.<strong>Step 5:</strong>Double the quotient and use it as the new<a>divisor</a>. </p>

20 <p><strong>Step 4:</strong>Bring down the remainder (17) and add two zeros. Add a<a>decimal</a>point to the quotient, it becomes 10.0.<strong>Step 5:</strong>Double the quotient and use it as the new<a>divisor</a>. </p>

22 <p><strong>Step 6:</strong>Pick a number that will complete the divisor so that when it is multiplied by. The<a>product</a>will be less than or equal to 1700. </p>

21 <p><strong>Step 6:</strong>Pick a number that will complete the divisor so that when it is multiplied by. The<a>product</a>will be less than or equal to 1700. </p>

23 <p><strong>Step 7:</strong>Continue to the division to find the √117 to as many decimal places as necessary. → √117 = 10.816653 </p>

22 <p><strong>Step 7:</strong>Continue to the division to find the √117 to as many decimal places as necessary. → √117 = 10.816653 </p>

24 <h3>Square root of 117 using the approximation method</h3>

23 <h3>Square root of 117 using the approximation method</h3>

25 <p>In the approximation method, we estimate the square root by considering the closest perfect square to 117. Follow the below steps; </p>

24 <p>In the approximation method, we estimate the square root by considering the closest perfect square to 117. Follow the below steps; </p>

26 <p><strong>Step 1:</strong>Nearest perfect square to 117 → √100=10 and √121=11</p>

25 <p><strong>Step 1:</strong>Nearest perfect square to 117 → √100=10 and √121=11</p>

27 <p><strong>Step 2:</strong>117 falls between 100 and 121 therefore the square root falls between 10 and 11</p>

26 <p><strong>Step 2:</strong>117 falls between 100 and 121 therefore the square root falls between 10 and 11</p>

28 <p><strong>Step 3:</strong>We try to test numbers like 10.5,10.6 and further. We find that √117 = 10.816. </p>

27 <p><strong>Step 3:</strong>We try to test numbers like 10.5,10.6 and further. We find that √117 = 10.816. </p>

29 <h2>Common mistakes when finding the square root of 117</h2>

28 <h2>Common mistakes when finding the square root of 117</h2>

30 <p>Here are a few common mistakes that one can commit while learning to find the square root of 117. You can avoid them by making a note of the below; </p>

29 <p>Here are a few common mistakes that one can commit while learning to find the square root of 117. You can avoid them by making a note of the below; </p>

30 + <h2>Download Worksheets</h2>

31 <h3>Problem 1</h3>

32 <p>Find x²+3. x = √117.</p>

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

34 <p>x = √117 = 10.816 </p>

35 <p>x2 = 117 </p>

36 <p>X2+3 = 117+3 = 120 </p>

37 <h3>Explanation</h3>

38 <p> the value of x2+3 is 120. </p>

39 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

41 <p>Simplify 7√117+ 5√117.</p>

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

43 <p>→ Factor √117</p>

44 <p>7√117+ 5√117 </p>

45 <p>= √117(7+5) </p>

46 <p>= 12×10.816</p>

47 <p> = 129.792 </p>

48 <h3>Explanation</h3>

49 <p> 7√117+ 5√117 when simplified is 129.792 </p>

50 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

52 <p>The area of a square is 117 cm². Find the length of the side.</p>

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

54 <p>Area = s2 </p>

55 <p>Area = 117 cm2</p>

56 <p>s = √117</p>

57 <p>= 10.816 cm </p>

58 <h3>Explanation</h3>

59 <p>the length of the side is 10.816 cm </p>

60 <p>Well explained 👍</p>

61 <h2>FAQs on the square root of 117</h2>

62 <h3>1.What perfect square root into 117?</h3>

63 <p>All perfect squares below 117 are 1,4,9,16,25,36,49,64,81,100. </p>

64 <h3>2.What are the factors of 117?</h3>

65 <p>Factors - 1,3,9,13,39 and 117. </p>

66 <h3>3.Is 117 a composite number?</h3>

67 <h3>4.Is 4096 a perfect square?</h3>

68 <p>4096 is not a perfect square. It has an irrational root. </p>

69 <h3>5.What is the prime factorization of 117?</h3>

70 <h2>Important Glossaries for Square Root of 32</h2>

71 <ul><li><strong>Prime numbers -</strong>Any number that has only two factors, 1 and the number itself, is called a prime number. Prime numbers up to 10 are - 2,3,5,7.</li>

72 </ul><ul><li><strong>Integer -</strong>A number between zero and infinite, that can be positive or negative, fraction or decimal. </li>

73 </ul><ul><li><strong>Rational numbers -</strong>A number that can be expressed in p/q form and where both p and q are integers and q (the denominator) is not equal to 0. </li>

74 </ul><ul><li><strong>Irrational numbers -</strong>A number that cannot be expressed in the p/q form where q is equal to 0 is called an irrational number. </li>

75 </ul><ul><li><strong>Perfect square number -</strong>a number whose square root has no decimal places in them. </li>

76 </ul><ul><li><strong>Non-perfect square numbers -</strong>A number whose square has a fraction or decimal in its result. </li>

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

78 <p>▶</p>

79 <h2>Jaskaran Singh Saluja</h2>

80 <h3>About the Author</h3>

81 <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>

82 <h3>Fun Fact</h3>

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