Square Root of 7/3
2026-02-28 06:13 Diff
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Last updated on August 5, 2025

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.

What is the Square Root of 7/3?

The square root is the inverse of the square of a number. 7/3 is not a perfect square. The square root of 7/3 is expressed in both radical and exponential form. 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 irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 7/3

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

  • Long division method
  • Approximation method

Square Root of 7/3 by Long Division Method

The long division 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 square root using the long division method, step by step.

Step 1: Convert the fraction 7/3 into a decimal, approximately 2.333.

Step 2: 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.

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

Step 4: 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.

Step 5: 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.

Step 6: Subtract 133 - 125 (25 × 5) to get 8 and the quotient is 1.5.

Step 7: 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.

Step 8: Find the new divisor, which is 31, because 31 × 2 gives a number less than 80.

Step 9: Subtract 800 - 775 (31 × 25) to get the remainder 25.

Step 10: Continue these steps until you get two decimal places.

The square root of √(7/3) is approximately 1.5275.

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Square Root of 7/3 by Approximation Method

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.

Step 1: Convert 7/3 into a decimal, approximately 2.333.

Step 2: 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.

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

Step 4: 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.

Common Mistakes and How to Avoid Them in the Square Root of 7/3

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.

Problem 1

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

Okay, lets begin

The area of the square is approximately 2.333 square units.

Explanation

The area of the square = side².

The side length is given as √(7/3).

Area of the square = (√(7/3))² = 7/3 ≈ 2.333.

Therefore, the area of the square box is approximately 2.333 square units.

Well explained 👍

Problem 2

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?

Okay, lets begin

Approximately 1.1665 square feet

Explanation

We can divide the given area by 2 as the plot is square-shaped.

Dividing 7/3 by 2 = 7/6 ≈ 1.1665.

So half of the plot measures approximately 1.1665 square feet.

Well explained 👍

Problem 3

Calculate √(7/3) × 5.

Okay, lets begin

7.6375

Explanation

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

The second step is to multiply 1.5275 by 5.

So 1.5275 × 5 = 7.6375.

Well explained 👍

Problem 4

What will be the square root of (7/3 + 1)?

Okay, lets begin

The square root is approximately 1.8257.

Explanation

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

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

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

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length 'l' is √(7/3) units and the width 'w' is 3 units.

Okay, lets begin

We find the perimeter of the rectangle as 9.055 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

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

Well explained 👍

FAQ on Square Root of 7/3

1.What is √(7/3) in its simplest form?

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

2.Mention the factors of 7/3.

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

3.Calculate the square of 7/3.

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

4.Is 7/3 a prime number?

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

5.Is 7/3 an irrational number?

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

Important Glossaries for the Square Root of 7/3

  • Square root: 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.
  • Irrational number: 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.
  • Principal square root: 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.
  • Rational number: A number that can be expressed as the quotient or fraction p/q of two integers, where the denominator q is not zero.
  • Decimal: 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.

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Jaskaran Singh Saluja

About the Author

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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.