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

3 <p>If a number is multiplied by the same number, the result is a square. The inverse of a square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 16/36.</p>

4 <h2>What is the Square Root of 16/36?</h2>

5 <p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 16/36 is a<a>perfect square</a><a>fraction</a>. The square root of 16/36 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(16/36), whereas (16/36)^(1/2) in the exponential form. √(16/36) = 2/3, which is a<a>rational number</a>because it can be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>

6 <h2>Finding the Square Root of 16/36</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. Since 16/36 is a perfect square fraction, we can use the prime factorization method to find its<a>square root</a>. Let us now learn the following methods:</p>

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

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

10 <li>Approximation method</li>

11 </ul><h3>Square Root of 16/36 by Prime Factorization Method</h3>

12 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 16/36 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 16 and 36 16 can be broken down into 2 x 2 x 2 x 2, which is 2^4. 36 can be broken down into 2 x 2 x 3 x 3, which is 2^2 x 3^2.</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 16 and 36. Since both numbers are perfect squares, we can find the square root easily. √(16/36) = √(2^4 / 2^2 x 3^2) = √(2^2 / 3^2) = 2/3, as both the<a>numerator and denominator</a>can be paired perfectly.</p>

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17 <h3>Square Root of 16/36 by Long Division Method</h3>

16 <h3>Square Root of 16/36 by Long Division Method</h3>

18 <p>The<a>long division</a>method is typically used for non-perfect square numbers, but it can also be applied to perfect square fractions for verification. Here’s how you can find the square root of 16/36 using the long division method:</p>

17 <p>The<a>long division</a>method is typically used for non-perfect square numbers, but it can also be applied to perfect square fractions for verification. Here’s how you can find the square root of 16/36 using the long division method:</p>

19 <p><strong>Step 1:</strong>Divide 16 by 36, which simplifies to 0.4444...</p>

18 <p><strong>Step 1:</strong>Divide 16 by 36, which simplifies to 0.4444...</p>

20 <p><strong>Step 2:</strong>Find the square root of 0.4444... using long division:</p>

19 <p><strong>Step 2:</strong>Find the square root of 0.4444... using long division:</p>

21 <p><strong>Step 3:</strong>Group the numbers from right to left in pairs, here we start with 0.44.</p>

20 <p><strong>Step 3:</strong>Group the numbers from right to left in pairs, here we start with 0.44.</p>

22 <p><strong>Step 4:</strong>Find a number whose square is<a>less than</a>or equal to 44. In this case, 6^2 = 36.</p>

21 <p><strong>Step 4:</strong>Find a number whose square is<a>less than</a>or equal to 44. In this case, 6^2 = 36.</p>

23 <p><strong>Step 5:</strong>Subtract 36 from 44, giving a<a>remainder</a>of 8. Bring down two zeroes, making it 800.</p>

22 <p><strong>Step 5:</strong>Subtract 36 from 44, giving a<a>remainder</a>of 8. Bring down two zeroes, making it 800.</p>

24 <p><strong>Step 6:</strong>Doubling the result 6, we get 12. Find the next digit in the result, making it 12x, where x is chosen to fit 800.</p>

23 <p><strong>Step 6:</strong>Doubling the result 6, we get 12. Find the next digit in the result, making it 12x, where x is chosen to fit 800.</p>

25 <p><strong>Step 7:</strong>Continue the process to get the<a>decimal</a>approximation, which will eventually lead you to 0.6666...</p>

24 <p><strong>Step 7:</strong>Continue the process to get the<a>decimal</a>approximation, which will eventually lead you to 0.6666...</p>

26 <h3>Square Root of 16/36 by Approximation Method</h3>

25 <h3>Square Root of 16/36 by Approximation Method</h3>

27 <p>Approximation method is another technique for finding square roots, particularly useful for verifying results. Here is how we approximate the square root of 16/36:</p>

26 <p>Approximation method is another technique for finding square roots, particularly useful for verifying results. Here is how we approximate the square root of 16/36:</p>

28 <p><strong>Step 1:</strong>Recognize that 16/36 simplifies to 4/9, which are both perfect squares.</p>

27 <p><strong>Step 1:</strong>Recognize that 16/36 simplifies to 4/9, which are both perfect squares.</p>

29 <p><strong>Step 2:</strong>Calculate the square roots: √16 = 4 and √36 = 6.</p>

28 <p><strong>Step 2:</strong>Calculate the square roots: √16 = 4 and √36 = 6.</p>

30 <p><strong>Step 3:</strong>Therefore, the square root of 16/36 is 4/6, which simplifies to 2/3. Thus, √(16/36) = 2/3, confirming the exact value.</p>

29 <p><strong>Step 3:</strong>Therefore, the square root of 16/36 is 4/6, which simplifies to 2/3. Thus, √(16/36) = 2/3, confirming the exact value.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 16/36</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 16/36</h2>

32 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or not simplifying fractions properly. Let us look at a few of those mistakes that students tend to make in detail.</p>

31 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or not simplifying fractions properly. Let us look at a few of those mistakes that students tend to make in detail.</p>

33 <h3>Problem 1</h3>

32 <h3>Problem 1</h3>

34 <p>Can you help Max find the area of a square box if its side length is given as √(25/49)?</p>

33 <p>Can you help Max find the area of a square box if its side length is given as √(25/49)?</p>

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

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

36 <p>The area of the square is 25/49 square units.</p>

35 <p>The area of the square is 25/49 square units.</p>

37 <h3>Explanation</h3>

36 <h3>Explanation</h3>

38 <p>The area of the square = side^2.</p>

37 <p>The area of the square = side^2.</p>

39 <p>The side length is given as √(25/49).</p>

38 <p>The side length is given as √(25/49).</p>

40 <p>Area of the square = side^2 = (√(25/49))^2 = 25/49.</p>

39 <p>Area of the square = side^2 = (√(25/49))^2 = 25/49.</p>

41 <p>Therefore, the area of the square box is 25/49 square units.</p>

40 <p>Therefore, the area of the square box is 25/49 square units.</p>

42 <p>Well explained 👍</p>

41 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

42 <h3>Problem 2</h3>

44 <p>A square-shaped building measuring 16/36 square feet is built; if each of the sides is √(16/36), what will be the square feet of half of the building?</p>

43 <p>A square-shaped building measuring 16/36 square feet is built; if each of the sides is √(16/36), what will be the square feet of half of the building?</p>

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

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

46 <p>8/36 square feet</p>

45 <p>8/36 square feet</p>

47 <h3>Explanation</h3>

46 <h3>Explanation</h3>

48 <p>We can just divide the given area by 2 as the building is square-shaped.</p>

47 <p>We can just divide the given area by 2 as the building is square-shaped.</p>

49 <p>Dividing 16/36 by 2 = 8/36.</p>

48 <p>Dividing 16/36 by 2 = 8/36.</p>

50 <p>So half of the building measures 8/36 square feet.</p>

49 <p>So half of the building measures 8/36 square feet.</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

51 <h3>Problem 3</h3>

53 <p>Calculate √(16/36) x 5.</p>

52 <p>Calculate √(16/36) x 5.</p>

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

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

55 <p>10/3</p>

54 <p>10/3</p>

56 <h3>Explanation</h3>

55 <h3>Explanation</h3>

57 <p>The first step is to find the square root of 16/36, which is 2/3.</p>

56 <p>The first step is to find the square root of 16/36, which is 2/3.</p>

58 <p>The second step is to multiply 2/3 by 5.</p>

57 <p>The second step is to multiply 2/3 by 5.</p>

59 <p>So (2/3) x 5 = 10/3.</p>

58 <p>So (2/3) x 5 = 10/3.</p>

60 <p>Well explained 👍</p>

59 <p>Well explained 👍</p>

61 <h3>Problem 4</h3>

60 <h3>Problem 4</h3>

62 <p>What will be the square root of (9/16 + 1/4)?</p>

61 <p>What will be the square root of (9/16 + 1/4)?</p>

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

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

64 <p>The square root is 3/4</p>

63 <p>The square root is 3/4</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>To find the square root, we need to find the sum of (9/16 + 1/4).</p>

65 <p>To find the square root, we need to find the sum of (9/16 + 1/4).</p>

67 <p>Convert 1/4 to 4/16 to have a common denominator: 9/16 + 4/16 = 13/16.</p>

66 <p>Convert 1/4 to 4/16 to have a common denominator: 9/16 + 4/16 = 13/16.</p>

68 <p>Therefore, the square root of (13/16) is approximately ±3/4 when considering the closest simple fraction.</p>

67 <p>Therefore, the square root of (13/16) is approximately ±3/4 when considering the closest simple fraction.</p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h3>Problem 5</h3>

69 <h3>Problem 5</h3>

71 <p>Find the perimeter of a rectangle if its length 'l' is √(16/36) units and the width 'w' is 3 units.</p>

70 <p>Find the perimeter of a rectangle if its length 'l' is √(16/36) units and the width 'w' is 3 units.</p>

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

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

73 <p>We find the perimeter of the rectangle as 14/3 units.</p>

72 <p>We find the perimeter of the rectangle as 14/3 units.</p>

74 <h3>Explanation</h3>

73 <h3>Explanation</h3>

75 <p>Perimeter of the rectangle = 2 × (length + width).</p>

74 <p>Perimeter of the rectangle = 2 × (length + width).</p>

76 <p>Perimeter = 2 × (√(16/36) + 3) = 2 × (2/3 + 3) = 2 × (11/3) = 22/3 units.</p>

75 <p>Perimeter = 2 × (√(16/36) + 3) = 2 × (2/3 + 3) = 2 × (11/3) = 22/3 units.</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h2>FAQ on Square Root of 16/36</h2>

77 <h2>FAQ on Square Root of 16/36</h2>

79 <h3>1.What is √(16/36) in its simplest form?</h3>

78 <h3>1.What is √(16/36) in its simplest form?</h3>

80 <p>The prime factorization of 16 is 2 x 2 x 2 x 2 and for 36, it is 2 x 2 x 3 x 3.</p>

79 <p>The prime factorization of 16 is 2 x 2 x 2 x 2 and for 36, it is 2 x 2 x 3 x 3.</p>

81 <p>Thus, the simplest form of √(16/36) is 2/3.</p>

80 <p>Thus, the simplest form of √(16/36) is 2/3.</p>

82 <h3>2.Mention the factors of 16 and 36.</h3>

81 <h3>2.Mention the factors of 16 and 36.</h3>

83 <p>Factors of 16 are 1, 2, 4, 8, and 16.</p>

82 <p>Factors of 16 are 1, 2, 4, 8, and 16.</p>

84 <p>Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.</p>

83 <p>Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.</p>

85 <h3>3.Calculate the product of 16 and 36.</h3>

84 <h3>3.Calculate the product of 16 and 36.</h3>

86 <p>We get the product by multiplying the numbers: 16 x 36 = 576.</p>

85 <p>We get the product by multiplying the numbers: 16 x 36 = 576.</p>

87 <h3>4.Are 16 and 36 prime numbers?</h3>

86 <h3>4.Are 16 and 36 prime numbers?</h3>

88 <p>Neither 16 nor 36 is a<a>prime number</a>, as both have more than two factors.</p>

87 <p>Neither 16 nor 36 is a<a>prime number</a>, as both have more than two factors.</p>

89 <h3>5.What is the simplest form of 16/36?</h3>

88 <h3>5.What is the simplest form of 16/36?</h3>

90 <p>The simplest form of 16/36 is 4/9, as both 16 and 36 can be divided by 4.</p>

89 <p>The simplest form of 16/36 is 4/9, as both 16 and 36 can be divided by 4.</p>

91 <h2>Important Glossaries for the Square Root of 16/36</h2>

90 <h2>Important Glossaries for the Square Root of 16/36</h2>

92 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.<strong></strong></li>

91 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.<strong></strong></li>

93 </ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, where p and q are integers and q ≠ 0.</li>

92 </ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, where p and q are integers and q ≠ 0.</li>

94 </ul><ul><li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it equals 4^2.</li>

93 </ul><ul><li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it equals 4^2.</li>

95 </ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as a product of its prime factors. For example, the prime factorization of 36 is 2^2 x 3^2.<strong></strong></li>

94 </ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as a product of its prime factors. For example, the prime factorization of 36 is 2^2 x 3^2.<strong></strong></li>

96 </ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole or any number of equal parts. It is represented as p/q, where p is the numerator and q is the denominator.</li>

95 </ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole or any number of equal parts. It is represented as p/q, where p is the numerator and q is the denominator.</li>

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

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

98 <p>▶</p>

97 <p>▶</p>

99 <h2>Jaskaran Singh Saluja</h2>

98 <h2>Jaskaran Singh Saluja</h2>

100 <h3>About the Author</h3>

99 <h3>About the Author</h3>

101 <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>

100 <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>

102 <h3>Fun Fact</h3>

101 <h3>Fun Fact</h3>

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

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