101 LearnersLast updated on May 26th, 2025
Square Root of 2.25
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 2.25.
What is the Square Root of 2.25?
The square root is the inverse of the square of the number. 2.25 is a perfect square. The square root of 2.25 is expressed in both radical and exponential form. In radical form, it is expressed as √2.25, whereas (2.25)^(1/2) in exponential form. √2.25 = 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 2.25
The prime factorization method is used for perfect square numbers. Since 2.25 is a perfect square, we can use the prime factorization method or the approximation method to find its square root. Let us learn these methods:
- Prime factorization method
- Approximation method
Square Root of 2.25 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2.25 is broken down into its prime factors.
Step 1: Express 2.25 as a fraction, 225/100.
Step 2: Prime factorize both the numerator and the denominator. 225 = 3 × 3 × 5 × 5 = 3^2 × 5^2 100 = 2 × 2 × 5 × 5 = 2^2 × 5^2
Step 3: Taking the square root of both the numerator and the denominator: √(225/100) = (3 × 5)/(2 × 5) = 3/2
Thus, √2.25 = 1.5.
Square Root of 2.25 by Approximation Method
The approximation method is another way to find square roots, especially when the number is not easily factorized. However, since 2.25 is a perfect square, we can easily approximate its square root.
Step 1: Recognize that 2.25 is close to 2 and 4, both perfect squares.
Step 2: The square root of 2 is approximately 1.41, and the square root of 4 is 2.
Step 3: Since 2.25 is halfway between 2 and 4, its square root will be halfway between 1.41 and 2, which is 1.5.
Common Mistakes and How to Avoid Them in the Square Root of 2.25
Students might make mistakes while finding the square root, such as miscalculating the prime factorization or not recognizing the perfect square. Now let us look at a few common mistakes in detail.
Square Root of 2.25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2.25?
The area of the square is 2.25 square units.
Explanation
The area of the square = side^2.
The side length is given as √2.25.
Area of the square = side^2 = √2.25 × √2.25 = 1.5 × 1.5 = 2.25
Therefore, the area of the square box is 2.25 square units.
Problem 2
A square-shaped building measuring 2.25 square feet is built; if each of the sides is √2.25, what will be the square feet of half of the building?
1.125 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2.25 by 2 = we get 1.
125 So half of the building measures 1.125 square feet.
Problem 3
Calculate √2.25 × 5.
7.5
Explanation
The first step is to find the square root of 2.25, which is 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 (2 + 0.25)?
The square root is 1.5.
Explanation
To find the square root, we need to find the sum of (2 + 0.25).
2 + 0.25 = 2.25, and then √2.25 = 1.5.
Therefore, the square root of (2 + 0.25) is ±1.5.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √2.25 units and the width ‘w’ is 3 units.
We find the perimeter of the rectangle as 9 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2.25 + 3)
= 2 × (1.5 + 3)
= 2 × 4.5
= 9 units.
FAQ on Square Root of 2.25
1.What is √2.25 in its simplest form?
2.Is 2.25 a perfect square?
3.Calculate the square of 2.25.
4.Is 2.25 a rational number?
5.What is the decimal representation of √2.25?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 2.25?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 2.25?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 2.25
- Square root: A square root is the inverse of a square. Example: 1.5^2 = 2.25, and the inverse of the square is the square root, which is √2.25 = 1.5.
- 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 number is a perfect square if its square root is an integer or a simple fraction (like 1.5 for 2.25).
- Factorization: Breaking down a number into its prime factors. For example, 225 = 3^2 × 5^2.
- Decimal: A number that has a whole number and a fractional part, separated by a decimal point, for example, 1.5.
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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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