121 LearnersLast updated on May 26th, 2025
Square Root of 9/4
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
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
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.
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.
Mistake 1
Forgetting about the negative square root
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.
Mistake 2
Not simplifying fractions correctly
Mistakes can occur if fractions are not simplified correctly. For instance, failing to simplify 9/4 before finding the square root can lead to errors. Always simplify fractions where possible.
Mistake 3
Confusing square roots with other operations
Students might confuse square roots with other operations such as division or multiplication.
For example, √(9/4) should not be confused with (9/4)/2 or (9/4)*2.
Mistake 4
Ignoring the properties of square roots
Students need to remember that the square root of a fraction is the square root of the numerator divided by the square root of the denominator.
For example, √(9/4) = √9/√4.
Mistake 5
Misidentifying perfect squares
Misidentifying numbers as perfect squares can lead to incorrect solutions. Always verify whether the numerator and denominator are perfect squares before proceeding.
Square Root of 9/4 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(9/4)?
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.
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?
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.
Problem 3
Calculate √(9/4) × 5.
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.
Problem 4
What will be the square root of (9 + 1)?
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.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √(9/4) units and the width ‘w’ is 5 units.
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.
FAQ on Square Root of 9/4
1.What is √(9/4) in its simplest form?
2.Is 9/4 a perfect square?
3.Calculate the square of 9/4.
4.Is 9/4 a rational number?
5.What is the decimal form of 9/4?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 9/4?
8.How do technology and digital tools in India support learning Algebra and Square Root of 9/4?
9.Does learning Algebra support future career opportunities for students in India?
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
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