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558 LearnersLast updated on August 5, 2025
Square Root of 9/2
What is the Square Root of 9/2?
The square root is the inverse of the square of the number. 9/2 is not a perfect square. The square root of 9/2 is expressed in both radical and exponential form. In radical form, it is expressed as √(9/2), whereas (9/2)^(1/2) in exponential form. √(9/2) = √(4.5) = 2.12132, 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 9/2
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not typically used for non-perfect square numbers where long-division and approximation methods are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 9/2 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we find the square root step by step. Let us see how to find the square root of 9/2 using the long division method:
Step 1: Convert the fraction to a decimal, which is 4.5.
Step 2: Find a number whose square is closest to 4.5.
Step 3: The square root of 4 is 2, which is the closest lower perfect square.
Step 4: Use the long division process to refine the result and find the decimal points.
The square root of 4.5 is approximately 2.12132.
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Square Root of 9/2 by Approximation Method
The approximation method is another way to find square roots. It is an easier method to find the square root of a given number. Now let us learn how to find the square root of 9/2 using the approximation method.
Step 1: Convert 9/2 to a decimal, which is 4.5.
Step 2: Find the closest perfect squares around 4.5. The smallest perfect square less than 4.5 is 4, and the largest perfect square greater than 4.5 is 9. Therefore, √4.5 falls between 2 and 3.
Step 3: Use the approximation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (4.5 - 4) / (9 - 4) = 0.1
Step 4: Add this to the lower bound (2 + 0.1 = 2.1).
Thus, the square root of 4.5 is approximately 2.12132.
Common Mistakes and How to Avoid Them in the Square Root of 9/2
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division. Let us look at a few common mistakes 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.
For example, √(9/2) = ±2.12132. However, unless specified, the principal (positive) square root is generally used.
Mistake 2
Not adding the square root symbol in proper places
A common mistake is incorrectly using the square root symbol.
For example, √(4.5) should not be mistakenly written as √4 + √0.5. The correct representation is √(4.5).
Mistake 3
Not finding the correct value of a non-perfect square
It's crucial to simplify and accurately calculate the square root of non-perfect squares.
For example, stating √4.5 ≈ 2 is incorrect; the approximate value is 2.12132.
Mistake 4
Confusing the square root symbol with the cube root
Students should be aware of the difference between square roots and cube roots (e.g., √4.5 vs. ∛4.5).
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves several steps. Skipping a step or making a calculation error can lead to incorrect results.
Square Root of 9/2 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(9/2)?
The area of the square is approximately 4.5 square units.
Explanation
The area of a square = side².
The side length is given as √(9/2).
Area = (√(9/2))² = 9/2 = 4.5 square units.
Therefore, the area of the square box is approximately 4.5 square units.
Problem 2
A square-shaped building measuring 9/2 square feet is built; if each of the sides is √(9/2), what will be the square feet of half of the building?
2.25 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 9/2 by 2 = 9/4 = 2.25 square feet.
So half of the building measures 2.25 square feet.
Problem 3
Calculate √(9/2) x 5.
10.6066
Explanation
First, find the square root of 9/2, which is approximately 2.12132.
Then multiply by 5.
So, 2.12132 x 5 = 10.6066.
Problem 4
What will be the square root of (9/2 + 2)?
The square root is approximately 2.54951.
Explanation
To find the square root, first find the sum of (9/2 + 2) = 4.5 + 2 = 6.5.
The square root of 6.5 is approximately 2.54951.
Therefore, the square root of (9/2 + 2) is ±2.54951.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(9/2) units and the width ‘w’ is 2 units.
We find the perimeter of the rectangle as approximately 8.24264 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(9/2) + 2) ≈ 2 × (2.12132 + 2) ≈ 2 × 4.12132 ≈ 8.24264 units.
FAQ on Square Root of 9/2
1.What is √(9/2) in its simplest form?
2.What are the factors of 9/2?
3.Calculate the square of 9/2.
4.Is 9/2 a rational number?
5.Is 9/2 divisible by any integer?
Important Glossaries for the Square Root of 9/2
- Square root: The square root is the inverse operation of squaring a number. For example, if 4 is squared to get 16, then the square root of 16 is 4.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction of two integers. For example, √2 is irrational.
- Principal square root: The principal square root of a non-negative number is the non-negative root. For example, the principal square root of 9 is 3.
- Fraction: A fraction represents a part of a whole and consists of a numerator and a denominator. For example, 1/2.
- Decimal: A decimal number is a representation of a fraction using powers of ten. For example, 0.5 is the decimal representation of 1/2.
Vikrant Sharma
About the Author
Vikrant is a passionate Mathematics teacher with over 5 years of teaching experience in both conventional and Vedic Maths. His student-focused approach combines clear concepts with motivation and encouragement, helping students build confidence and develo
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
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