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

3 <p>If a number is multiplied by itself, the result is a square. The inverse of a square is a square root. Square roots are used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 7/3.</p>

4 <h2>What is the Square Root of 7/3?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 7/3 is not a<a>perfect square</a>. The square root of 7/3 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(7/3), whereas (7/3)^(1/2) in the exponential form. √(7/3) approximately equals 1.5275, which is an<a>irrational number</a>because it cannot 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 7/3</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the<a>long division</a>method and approximation method are used. Let us now learn the following methods:</p>

8 <ul><li>Long division method</li>

9 <li>Approximation method</li>

10 </ul><h2>Square Root of 7/3 by Long Division Method</h2>

11 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

12 <p><strong>Step 1:</strong>Convert the<a>fraction</a>7/3 into a<a>decimal</a>, approximately 2.333.</p>

13 <p><strong>Step 2:</strong>To begin with, we need to group the numbers from right to left. In the case of 2.333, we need to group it as 2.33 and 0.03.</p>

14 <p><strong>Step 3:</strong>Now we need to find n whose square is<a>less than</a>or equal to 2.33. We can choose n as ‘1’ because 1 × 1 is lesser than or equal to 2.33. Now the<a>quotient</a>is 1 and the<a>remainder</a>is 1.33.</p>

15 <p><strong>Step 4:</strong>Bring down 0.03 to make it 133. Add the old divisor with the same number 1 + 1 to get 2 which will be our new divisor.</p>

16 <p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 133. Let us consider n as 6, now 26 × 6 = 156 which is more than 133, so we choose n as 5.</p>

17 <p><strong>Step 6:</strong>Subtract 133 - 125 (25 × 5) to get 8 and the quotient is 1.5.</p>

18 <p><strong>Step 7:</strong>Since the dividend is less than the divisor, we add a decimal point. Adding a decimal point allows us to add two zeroes to the dividend. Now the new dividend is 800.</p>

19 <p><strong>Step 8:</strong>Find the new divisor, which is 31, because 31 × 2 gives a number less than 80.</p>

20 <p><strong>Step 9:</strong>Subtract 800 - 775 (31 × 25) to get the remainder 25.</p>

21 <p><strong>Step 10:</strong>Continue these steps until you get two decimal places.</p>

22 <p>The square root of √(7/3) is approximately 1.5275.</p>

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25 <h2>Square Root of 7/3 by Approximation Method</h2>

24 <h2>Square Root of 7/3 by Approximation Method</h2>

26 <p>The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 7/3 using the approximation method.</p>

25 <p>The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 7/3 using the approximation method.</p>

27 <p><strong>Step 1:</strong>Convert 7/3 into a decimal, approximately 2.333.</p>

26 <p><strong>Step 1:</strong>Convert 7/3 into a decimal, approximately 2.333.</p>

28 <p><strong>Step 2:</strong>Find the closest perfect squares around 2.333. The smallest perfect square is 1 and the largest is 4. √(7/3) falls somewhere between 1 and 2.</p>

27 <p><strong>Step 2:</strong>Find the closest perfect squares around 2.333. The smallest perfect square is 1 and the largest is 4. √(7/3) falls somewhere between 1 and 2.</p>

29 <p><strong>Step 3:</strong>Apply the interpolation<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).Going by the formula: (2.333 - 1) / (4 - 1) = 0.444.</p>

28 <p><strong>Step 3:</strong>Apply the interpolation<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).Going by the formula: (2.333 - 1) / (4 - 1) = 0.444.</p>

30 <p><strong>Step 4:</strong>Using the formula, we identify the decimal point of our square root. Adding this to the smallest integer, 1 + 0.444 = 1.444, so the square root of 7/3 is approximately 1.5275.</p>

29 <p><strong>Step 4:</strong>Using the formula, we identify the decimal point of our square root. Adding this to the smallest integer, 1 + 0.444 = 1.444, so the square root of 7/3 is approximately 1.5275.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7/3</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7/3</h2>

32 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.</p>

31 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes 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 √(7/3)?</p>

33 <p>Can you help Max find the area of a square box if its side length is given as √(7/3)?</p>

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

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

36 <p>The area of the square is approximately 2.333 square units.</p>

35 <p>The area of the square is approximately 2.333 square units.</p>

37 <h3>Explanation</h3>

36 <h3>Explanation</h3>

38 <p>The area of the square = side².</p>

37 <p>The area of the square = side².</p>

39 <p>The side length is given as √(7/3).</p>

38 <p>The side length is given as √(7/3).</p>

40 <p>Area of the square = (√(7/3))² = 7/3 ≈ 2.333.</p>

39 <p>Area of the square = (√(7/3))² = 7/3 ≈ 2.333.</p>

41 <p>Therefore, the area of the square box is approximately 2.333 square units.</p>

40 <p>Therefore, the area of the square box is approximately 2.333 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 plot measuring 7/3 square feet is built; if each of the sides is √(7/3), what will be the square feet of half of the plot?</p>

43 <p>A square-shaped plot measuring 7/3 square feet is built; if each of the sides is √(7/3), what will be the square feet of half of the plot?</p>

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

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

46 <p>Approximately 1.1665 square feet</p>

45 <p>Approximately 1.1665 square feet</p>

47 <h3>Explanation</h3>

46 <h3>Explanation</h3>

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

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

49 <p>Dividing 7/3 by 2 = 7/6 ≈ 1.1665.</p>

48 <p>Dividing 7/3 by 2 = 7/6 ≈ 1.1665.</p>

50 <p>So half of the plot measures approximately 1.1665 square feet.</p>

49 <p>So half of the plot measures approximately 1.1665 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 √(7/3) × 5.</p>

52 <p>Calculate √(7/3) × 5.</p>

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

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

55 <p>7.6375</p>

54 <p>7.6375</p>

56 <h3>Explanation</h3>

55 <h3>Explanation</h3>

57 <p>The first step is to find the square root of 7/3, which is approximately 1.5275.</p>

56 <p>The first step is to find the square root of 7/3, which is approximately 1.5275.</p>

58 <p>The second step is to multiply 1.5275 by 5.</p>

57 <p>The second step is to multiply 1.5275 by 5.</p>

59 <p>So 1.5275 × 5 = 7.6375.</p>

58 <p>So 1.5275 × 5 = 7.6375.</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 (7/3 + 1)?</p>

61 <p>What will be the square root of (7/3 + 1)?</p>

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

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

64 <p>The square root is approximately 1.8257.</p>

63 <p>The square root is approximately 1.8257.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>To find the square root, we need to find the sum of (7/3 + 1).</p>

65 <p>To find the square root, we need to find the sum of (7/3 + 1).</p>

67 <p>7/3 + 1 = 10/3, and then √(10/3) ≈ 1.8257.</p>

66 <p>7/3 + 1 = 10/3, and then √(10/3) ≈ 1.8257.</p>

68 <p>Therefore, the square root of (7/3 + 1) is approximately 1.8257.</p>

67 <p>Therefore, the square root of (7/3 + 1) is approximately 1.8257.</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 √(7/3) units and the width 'w' is 3 units.</p>

70 <p>Find the perimeter of a rectangle if its length 'l' is √(7/3) 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 9.055 units.</p>

72 <p>We find the perimeter of the rectangle as 9.055 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 × (√(7/3) + 3) = 2 × (1.5275 + 3) = 2 × 4.5275 = 9.055 units.</p>

75 <p>Perimeter = 2 × (√(7/3) + 3) = 2 × (1.5275 + 3) = 2 × 4.5275 = 9.055 units.</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h2>FAQ on Square Root of 7/3</h2>

77 <h2>FAQ on Square Root of 7/3</h2>

79 <h3>1.What is √(7/3) in its simplest form?</h3>

78 <h3>1.What is √(7/3) in its simplest form?</h3>

80 <p>The fraction 7/3 is already in its simplest form, so the simplest form of √(7/3) is √(7/3).</p>

79 <p>The fraction 7/3 is already in its simplest form, so the simplest form of √(7/3) is √(7/3).</p>

81 <h3>2.Mention the factors of 7/3.</h3>

80 <h3>2.Mention the factors of 7/3.</h3>

82 <p>Since 7/3 is a fraction, it doesn't have traditional<a>factors</a>like integers do. It is expressed as a division of two<a>prime numbers</a>.</p>

81 <p>Since 7/3 is a fraction, it doesn't have traditional<a>factors</a>like integers do. It is expressed as a division of two<a>prime numbers</a>.</p>

83 <h3>3.Calculate the square of 7/3.</h3>

82 <h3>3.Calculate the square of 7/3.</h3>

84 <p>We get the square of 7/3 by multiplying the number by itself, that is (7/3) × (7/3) = 49/9 ≈ 5.4444.</p>

83 <p>We get the square of 7/3 by multiplying the number by itself, that is (7/3) × (7/3) = 49/9 ≈ 5.4444.</p>

85 <h3>4.Is 7/3 a prime number?</h3>

84 <h3>4.Is 7/3 a prime number?</h3>

86 <p>Since 7/3 is a fraction, the concept of prime numbers does not apply to it. Prime numbers are integers<a>greater than</a>1 that have no divisors other than 1 and themselves.</p>

85 <p>Since 7/3 is a fraction, the concept of prime numbers does not apply to it. Prime numbers are integers<a>greater than</a>1 that have no divisors other than 1 and themselves.</p>

87 <h3>5.Is 7/3 an irrational number?</h3>

86 <h3>5.Is 7/3 an irrational number?</h3>

88 <p>7/3 itself is not an irrational number; it is a<a>rational number</a>because it can be expressed as a fraction of two integers. However, its square root, √(7/3), is an irrational number.</p>

87 <p>7/3 itself is not an irrational number; it is a<a>rational number</a>because it can be expressed as a fraction of two integers. However, its square root, √(7/3), is an irrational number.</p>

89 <h2>Important Glossaries for the Square Root of 7/3</h2>

88 <h2>Important Glossaries for the Square Root of 7/3</h2>

90 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is, √16 = 4.</li>

89 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is, √16 = 4.</li>

91 </ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>

90 </ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>

92 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is the positive square root that is more commonly used due to its applications in the real world. This is known as the principal square root.</li>

91 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is the positive square root that is more commonly used due to its applications in the real world. This is known as the principal square root.</li>

93 </ul><ul><li><strong>Rational number:</strong>A number that can be expressed as the quotient or fraction p/q of two integers, where the denominator q is not zero.</li>

92 </ul><ul><li><strong>Rational number:</strong>A number that can be expressed as the quotient or fraction p/q of two integers, where the denominator q is not zero.</li>

94 </ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.</li>

93 </ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.</li>

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

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

96 <p>▶</p>

95 <p>▶</p>

97 <h2>Jaskaran Singh Saluja</h2>

96 <h2>Jaskaran Singh Saluja</h2>

98 <h3>About the Author</h3>

97 <h3>About the Author</h3>

99 <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>

98 <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 <h3>Fun Fact</h3>

99 <h3>Fun Fact</h3>

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

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