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1 - <p>730 Learners</p>

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

3 <p>The square root of 116 can be ‘x’ where we get 116 as a result when ‘y’ gets multiplied by y itself → y × y. The number 116 has a special square root called the principal square root.</p>

4 <h2>What is the square root of 116?</h2>

5 <p> ±10.77 is the<a>square</a>root of 116. To find the square root, we should use the inverse process of squaring a<a>number</a>. So, when 10.77 is squared, we get 116. The radical form of 116 is expressed as √116, where ‘√’ is the radical<a>symbol</a>. The square root of 116 is expressed in its<a>exponential form</a>as (116)½.</p>

6 <h2>Finding the Square Root of 116</h2>

7 <p>The<a>square root</a>of 116 can be calculated with the help of different methods such as:</p>

8 <ul><li>Prime Factorization Method</li>

9 </ul><ul><li>Long Division Method</li>

10 </ul><ul><li>Approximation or Estimation Method </li>

11 </ul><h3>Square Root of 116 By Prime Factorization</h3>

12 <p>The<a>prime factorization</a>of 116 is done by breaking 116 into its prime<a>factors</a>until the<a>quotient</a>can’t be divided anymore. </p>

13 <p>The prime factors of 116 are 2 and 29, expressed as 2×2×29 → 22 × 29</p>

14 <p>If a number exists that cannot be paired, then that number is written using the radical sign along with paired numbers. Hence, 2√29 is the simplest form of √116.</p>

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17 <h2>Square Root of 116 By Long division</h2>

16 <h2>Square Root of 116 By Long division</h2>

18 <p>The<a>long division</a>method is used to find the square root of non-<a>perfect squares</a>. This method involves dividing the<a>dividend</a>with divisors, which results in not just a quotient but also a<a>remainder</a>.</p>

17 <p>The<a>long division</a>method is used to find the square root of non-<a>perfect squares</a>. This method involves dividing the<a>dividend</a>with divisors, which results in not just a quotient but also a<a>remainder</a>.</p>

19 <p>To calculate √116:</p>

18 <p>To calculate √116:</p>

20 <p><strong>Step 1:</strong>Draw a horizontal above 116</p>

19 <p><strong>Step 1:</strong>Draw a horizontal above 116</p>

21 <p><strong>Step 2:</strong>Now find the closest perfect square that lies near to 116. The perfect square closest to 116 is 100 → 102</p>

20 <p><strong>Step 2:</strong>Now find the closest perfect square that lies near to 116. The perfect square closest to 116 is 100 → 102</p>

22 <p><strong>Step 3:</strong>Divide 116 by 10. The quotient will remain 10 and the remainder will be 16 (116-100)</p>

21 <p><strong>Step 3:</strong>Divide 116 by 10. The quotient will remain 10 and the remainder will be 16 (116-100)</p>

23 <p><strong>Step 4:</strong>Bring down the remainder 16 and add two zeros. Add a<a>decimal</a>point to the quotient, it turns to 10.0.</p>

22 <p><strong>Step 4:</strong>Bring down the remainder 16 and add two zeros. Add a<a>decimal</a>point to the quotient, it turns to 10.0.</p>

24 <p><strong>Step 5:</strong>Double the quotient and use it as the new<a>divisor</a>. Now pick a number that will complete the divisor so that when it is multiplied by, the<a>product</a>is less than or equal to 1600. </p>

23 <p><strong>Step 5:</strong>Double the quotient and use it as the new<a>divisor</a>. Now pick a number that will complete the divisor so that when it is multiplied by, the<a>product</a>is less than or equal to 1600. </p>

25 <p><strong>Step 6:</strong>Continue to the division to find the √116</p>

24 <p><strong>Step 6:</strong>Continue to the division to find the √116</p>

26 <h2>Square Root of 116 By Approximation</h2>

25 <h2>Square Root of 116 By Approximation</h2>

27 <p>The approximation method estimates the square root by considering the closest perfect square.</p>

26 <p>The approximation method estimates the square root by considering the closest perfect square.</p>

28 <p><strong>Step 1:</strong>Nearest perfect square to 116 is √100=10 and √121=11</p>

27 <p><strong>Step 1:</strong>Nearest perfect square to 116 is √100=10 and √121=11</p>

29 <p><strong>Step 2</strong>: 116 falls between 100 and 121 therefore the square root falls between 10 and 11</p>

28 <p><strong>Step 2</strong>: 116 falls between 100 and 121 therefore the square root falls between 10 and 11</p>

30 <p><strong>Step 3:</strong> We find that √116 = 10.77. </p>

29 <p><strong>Step 3:</strong> We find that √116 = 10.77. </p>

31 <h2>Common Mistakes and How to Avoid Them in square root of 116</h2>

30 <h2>Common Mistakes and How to Avoid Them in square root of 116</h2>

32 <p>some common mistakes with their solutions are given below:</p>

31 <p>some common mistakes with their solutions are given below:</p>

32 + <h2>Download Worksheets</h2>

33 <h3>Problem 1</h3>

34 <p>If a = √116, find the result for the equation a²- 10</p>

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

36 <p>The result will be 106 </p>

37 <h3>Explanation</h3>

38 <p> It’s already given that a = √116. Therefore, a2 = 116. According to the equation a2 - 10 → 116 - 10 = 106. </p>

39 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

41 <p>Simplify (√116 + √116) + √116</p>

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

43 <p>Solution: 126.7629 </p>

44 <h3>Explanation</h3>

45 <p>√116 is 10. 77.</p>

46 <p>So (√116+√116) x √116 is (10.77+10.77)x10.77 is 126.7629 </p>

47 <p>Well explained 👍</p>

48 <h3>Problem 3</h3>

49 <p>Calculate (10.77/10 + 10.77/9)</p>

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

51 <p> The result will be 2.273 </p>

52 <h3>Explanation</h3>

53 <p>10.77/10 gives 1.077 and 10,77/9 gives 1.196. So, (10.77/10 + 10.77/9) will give 2.273 as result. </p>

54 <p>Well explained 👍</p>

55 <h2>FAQs on square root of 116</h2>

56 <h3>1.What is a principal square root ?</h3>

57 <p>The unique non-negative square root of a number is known as the principal square root. For example, √116 is the principal square root. </p>

58 <h3>2.How can I find the square root of 4?</h3>

59 <p>The square root of 4 can be found using methods like prime factorization and long division. </p>

60 <h3>3.Can you tell whether the square root of 116 is rational or irrational?</h3>

61 <p>The square root of 116 is ±10.77. So, 10.77 is an<a>irrational number</a>because it cannot be obtained dividing two integers.</p>

62 <h3>4.Write the perfect square which is nearer to 116</h3>

63 <p>The perfect square is100, having 10 as its square root. When 10 is multiplied two times, we get 100. </p>

64 <h3>5.What is the value of √11 and check if it’s an irrational number</h3>

65 <p>The value for √11 is 3.32, which is an irrational number. It is an irrational number because it cannot be obtained dividing two integers. </p>

66 <h2>Important Glossaries for Square Root of 116</h2>

67 <ul><li><strong>Prime number:</strong>Numbers having two factors.</li>

68 </ul><ul><li><strong>Perfect square:</strong>Numbers whose square root include only whole numbers</li>

69 </ul><ul><li><strong>Prime Factorization:</strong> Process of expressing the product of prime numbers in exponential form.</li>

70 </ul><ul><li><strong>Non-perfect square:</strong>Numbers whose square root contains decimals. </li>

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

72 <p>▶</p>

73 <h2>Jaskaran Singh Saluja</h2>

74 <h3>About the Author</h3>

75 <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>

76 <h3>Fun Fact</h3>

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