Square Root of 9/4
2026-02-28 06:12 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9/4

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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 9/4.

What is the Square Root of 9/4?

The square root is the inverse of the square of the number. 9/4 is a perfect square. The square root of 9/4 is expressed in both radical and exponential forms. In the radical form, it is expressed as √(9/4), whereas (9/4)^(1/2) in the exponential form. √(9/4) = 3/2 = 1.5, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 9/4

Square Root of 9/4 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 9/4 is broken down into its prime factors.

Step 1: Finding the prime factors of 9 and 4 Breaking it down, 9 = 3 × 3 and 4 = 2 × 2.

Step 2: Now we pair the prime factors. The square root of 9 is 3 (since 3 × 3 = 9) and the square root of 4 is 2 (since 2 × 2 = 4).

Therefore, calculating √(9/4) using prime factorization gives us 3/2.

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Square Root of 9/4 by Long Division Method

The long division method is particularly used for non-perfect square numbers, but it can also be applied to fractions. Let us learn how to find the square root using the long division method, step by step.

Step 1: Consider the fraction 9/4. We can find the square root of the numerator and denominator separately.

Step 2: The square root of 9 is 3 and the square root of 4 is 2.

Step 3: Therefore, the square root of 9/4 is 3/2.

Square Root of 9/4 by Approximation Method

Approximation method is another method for finding square roots, especially useful for non-perfect squares, but not needed here as 9/4 is a perfect square. However, let us briefly consider this method.

Step 1: Identify the closest perfect squares to 9 and 4, which are 9 and 4 themselves.

Step 2: Since both the numerator and the denominator are perfect squares, the square root of 9/4 is exactly 3/2 or 1.5 without needing approximation.

Common Mistakes and How to Avoid Them in the Square Root of 9/4

Students may make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying fractions. Let's look at a few common errors in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(9/4)?

Okay, lets begin

The area of the square is 2.25 square units.

Explanation

The area of the square = side^2.

The side length is given as √(9/4).

Area of the square = (√(9/4))^2 = (3/2)^2 = 2.25.

Therefore, the area of the square box is 2.25 square units.

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Problem 2

A square-shaped building measuring 9/4 square meters is built; if each of the sides is √(9/4), what will be the square meters of half of the building?

Okay, lets begin

1.125 square meters

Explanation

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

Dividing 9/4 by 2 gives us 1.125.

So half of the building measures 1.125 square meters.

Well explained 👍

Problem 3

Calculate √(9/4) × 5.

Okay, lets begin

7.5

Explanation

The first step is to find the square root of 9/4, which is 3/2 or 1.5.

The second step is to multiply 1.5 by 5.

So 1.5 × 5 = 7.5.

Well explained 👍

Problem 4

What will be the square root of (9 + 1)?

Okay, lets begin

The square root is 3.162

Explanation

To find the square root, we need to find the sum of (9 + 1).

9 + 1 = 10, and then √10 ≈ 3.162.

Therefore, the square root of (9 + 1) is approximately ±3.162.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(9/4) units and the width ‘w’ is 5 units.

Okay, lets begin

The perimeter of the rectangle is 13 units.

Explanation

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

Perimeter = 2 × (√(9/4) + 5) = 2 × (1.5 + 5) = 2 × 6.5 = 13 units.

Well explained 👍

FAQ on Square Root of 9/4

1.What is √(9/4) in its simplest form?

The prime factorization of 9 is 3 × 3 and of 4 is 2 × 2. The simplest form of √(9/4) is 3/2 or 1.5.

2.Is 9/4 a perfect square?

Yes, 9/4 is a perfect square because both 9 and 4 are perfect squares.

3.Calculate the square of 9/4.

We get the square of 9/4 by multiplying the number by itself, that is (9/4) × (9/4) = 81/16.

4.Is 9/4 a rational number?

Yes, 9/4 is a rational number because it can be expressed as a fraction of two integers.

5.What is the decimal form of 9/4?

Important Glossaries for the Square Root of 9/4

  • Square root: A square root is the inverse of a square. Example: 3^2 = 9 and the inverse of the square is the square root, which is √9 = 3.
  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
  • Perfect square: A perfect square is a number that can be expressed as the square of an integer or a fraction. Example: 9/4 is a perfect square because it equals (3/2)^2.
  • Fraction: A fraction represents a part of a whole and is expressed as a numerator divided by a denominator, such as 9/4.
  • Numerator and Denominator: In a fraction, the numerator is the top number and the denominator is the bottom number. They represent how many parts of a whole are being considered.

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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.