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Last updated on May 26th, 2025

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Square Root of 9/4

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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.

Square Root of 9/4 for Australian Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

Finding the Square Root of 9/4

The square root of a fraction can be found by taking the square root of the numerator and the denominator separately. Let us now explore the methods:

 

  • Prime factorization method
  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Max Pointing Out Common Math Mistakes

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.

Mistake 1

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Forgetting about the negative square root

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It is important to remember that a number has both positive and negative square roots. However, we usually take only the positive square root unless otherwise specified.

For example, √(9/4) = 1.5, but there is also -1.5, which should not be forgotten.

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Square Root of 9/4 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

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

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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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Max, the Girl Character from BrightChamps

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?

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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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √(9/4) × 5.

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 9/4

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

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2.Is 9/4 a perfect square?

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3.Calculate the square of 9/4.

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4.Is 9/4 a rational number?

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

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6.How does learning Algebra help students in Australia make better decisions in daily life?

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7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 9/4?

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8.How do technology and digital tools in Australia support learning Algebra and Square Root of 9/4?

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9.Does learning Algebra support future career opportunities for students in Australia?

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Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in Australia

At BrightChamps, we believe algebra is more than symbols—it opens doors to endless opportunities! Our mission is to help children all over Australia gain important math skills, focusing today on the Square Root of 9/4 with a special emphasis on understanding square roots—in a lively, fun, and easy-to-grasp way. Whether your child is calculating the speed of a roller coaster at Luna Park Sydney, tracking cricket match scores, or managing their allowance for the newest gadgets, mastering algebra gives them the confidence to tackle everyday problems. Our interactive lessons make learning both simple and enjoyable. Since children in Australia learn in various ways, we adapt our approach to fit each learner’s style. From Sydney’s vibrant streets to the stunning Gold Coast beaches, BrightChamps brings math to life, making it relevant and exciting throughout Australia. Let’s make square roots a joyful part of every child’s math journey!
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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.

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Max, the Girl Character from BrightChamps

Fun Fact

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

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