Square Root of 5/9
2026-02-28 06:03 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5/9

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Last updated on August 5, 2025

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 5/9.

What is the Square Root of 5/9?

The square root is the inverse of the square of the number. 5/9 is not a perfect square. The square root of 5/9 is expressed in both radical and exponential form. In the radical form, it is expressed as, √(5/9), whereas (5/9)^(1/2) in the exponential form. √(5/9) = √5/√9 = √5/3, 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 5/9

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

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 5/9 by Prime Factorization Method

The prime factorization of 5 is simply 5, as it is a prime number. The prime factorization of 9 is 3 x 3. Now let us look at how 5/9 is broken down:

Step 1: Finding the prime factors of the numerator and the denominator For 5, we have 5 (as it is prime). For 9, we have 3 x 3.

Step 2: The square root of 5/9 is calculated by taking the square root of the numerator and the denominator separately. √(5/9) = √5/√(3 x 3) = √5/3.

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Square Root of 5/9 by Long Division Method

The long division method is particularly used for non-perfect square numbers. Since 5/9 is a fraction, we apply the square root to the numerator and denominator separately:

Step 1: The closest perfect square number to 5 is 4, and for 9, it is 9 itself.

Step 2: Using long division, we can approximate the square root of 5 as 2.236. The square root of 9 is exactly 3.

Step 3: The square root of 5/9 is approximately 2.236/3 = 0.7453.

Square Root of 5/9 by Approximation Method

The approximation method is another method for finding square roots; 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 5/9 using the approximation method.

Step 1: We know the square root of 5 is approximately 2.236 and the square root of 9 is 3.

Step 2: So the square root of 5/9 is approximately 2.236/3 = 0.7453.

Common Mistakes and How to Avoid Them in the Square Root of 5/9

Students do make mistakes while finding the square root, such as forgetting to simplify fractions first. Skipping important steps, etc. Now let us look at a few of those mistakes that students tend to make in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(5/9)?

Okay, lets begin

The area of the square is 5/9 square units.

Explanation

The area of the square = side^2.

The side length is given as √(5/9).

Area of the square = (√(5/9))^2

= 5/9.

Therefore, the area of the square box is 5/9 square units.

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Problem 2

A square-shaped building measuring 5/9 square feet is built; if each of the sides is √(5/9), what will be the square feet of half of the building?

Okay, lets begin

5/18 square feet

Explanation

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

Dividing 5/9 by 2, we get 5/18.

So half of the building measures 5/18 square feet.

Well explained 👍

Problem 3

Calculate √(5/9) x 5.

Okay, lets begin

3.7265

Explanation

The first step is to find the square root of 5/9, which is approximately 0.7453.

The second step is to multiply 0.7453 with 5.

So 0.7453 x 5 = 3.7265.

Well explained 👍

Problem 4

What will be the square root of (5 + 4/9)?

Okay, lets begin

The square root is approximately 2.291.

Explanation

To find the square root, we need to find the sum of (5 + 4/9).

5 + 4/9 = 49/9. Then √(49/9) = √49/√9 = 7/3 = 2.333.

Therefore, the square root of (5 + 4/9) is approximately 2.333.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(5/9) units and the width ‘w’ is 3 units.

Okay, lets begin

We find the perimeter of the rectangle as 6.4906 units.

Explanation

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

Perimeter = 2 × (√(5/9) + 3)

= 2 × (0.7453 + 3)

= 2 × 3.7453

= 6.4906 units.

Well explained 👍

FAQ on Square Root of 5/9

1.What is √(5/9) in its simplest form?

The square root of 5/9 is √(5/9) = √5/√9 = √5/3, which is already in its simplest form.

2.What are the prime factors of 9?

The prime factorization of 9 is 3 x 3.

3.Calculate the square of 5/9.

We get the square of 5/9 by multiplying the fraction by itself: (5/9) x (5/9) = 25/81.

4.Is 5/9 a perfect square?

No, 5/9 is not a perfect square as neither 5 nor 9 are perfect squares themselves.

5.What is the decimal equivalent of √(5/9)?

The decimal equivalent of √(5/9) is approximately 0.7453.

Important Glossaries for the Square Root of 5/9

  • Square root: 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.
     
  • 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.
     
  • Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts, for example, 5/9.
     
  • Numerator and Denominator: In a fraction, the numerator is the top number and the denominator is the bottom number. In 5/9, 5 is the numerator and 9 is the denominator.
     
  • Decimal: A decimal number is a number that consists of a whole number and a fractional part separated by a decimal point, for example, 0.7453.

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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.