139 LearnersLast updated on May 26th, 2025
Square Root of 9/2
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 9/2.
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.
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.
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?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 9/2?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 9/2?
9.Does learning Algebra support future career opportunities for students in Singapore?
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.
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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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