147 LearnersLast updated on May 26th, 2025
Square Root of 90.25
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 90.25.
What is the Square Root of 90.25?
The square root is the inverse of the square of the number. 90.25 is a perfect square. The square root of 90.25 is expressed in both radical and exponential form.
In the radical form, it is expressed as √90.25, whereas in the exponential form it is (90.25)(1/2). The square root of 90.25 is 9.5, 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 90.25
The prime factorization method is used for perfect square numbers. For non-perfect squares, methods such as the long-division method and approximation method are used. However, since 90.25 is a perfect square, we can directly find its square root. Let us now learn the following methods: -
- Prime factorization method
- Long division method
- Approximation method
Square Root of 90.25 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. 90.25 is a perfect square and can be expressed as (9.5)2.
Thus, the prime factorization method confirms that 90.25 is a perfect square, and its square root is 9.5.
Square Root of 90.25 by Long Division Method
The long division method can also be used for finding the square root of perfect squares. For 90.25, we can follow these steps:
Step 1: Group the numbers from right to left. For 90.25, we consider it as 90.25.
Step 2: Find a number whose square is closest to 90 without exceeding it. Here, that number is 9, because 9 × 9 = 81.
Step 3: Subtract 81 from 90, which gives 9. Bring down 25 to make it 925.
Step 4: Double the divisor (9) to get 18. Next, find a number n such that 18n × n is closest to 925 without exceeding it. Here, n is 5, because 185 × 5 = 925.
Step 5: Subtract 925 from 925, giving a remainder of 0. The quotient is 9.5.
So the square root of √90.25 is 9.5.
Square Root of 90.25 by Approximation Method
The approximation method is also an easy way to find the square root of a given number. Here, however, since 90.25 is a perfect square, we can directly approximate it as follows:
Step 1: Identify the number nearest to 90.25 that is a perfect square. Both 81 (92) and 100 (102) are near, but 90.25 is exactly 9.52.
Therefore, the square root of 90.25 is 9.5.
Common Mistakes and How to Avoid Them in the Square Root of 90.25
Students often make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly applying methods. Let's 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. However, we usually consider only the principal (positive) square root in practical applications.
For example, √90.25 = 9.5, and there is also -9.5, which should not be forgotten.
Square Root of 90.25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √90.25?
The area of the square is 90.25 square units.
Explanation
The area of the square = side2.
The side length is given as √90.25.
Area of the square = side2 = √90.25 × √90.25 = 9.5 × 9.5 = 90.25.
Therefore, the area of the square box is 90.25 square units.
Problem 2
A square-shaped building measuring 90.25 square feet is built; if each of the sides is √90.25, what will be the square feet of half of the building?
45.125 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped. Dividing 90.25 by 2 gives us 45.125.
So half of the building measures 45.125 square feet.
Problem 3
Calculate √90.25 × 5.
47.5
Explanation
The first step is to find the square root of 90.25, which is 9.5.
The second step is to multiply 9.5 by 5.
So 9.5 × 5 = 47.5.
Problem 4
What will be the square root of (81 + 9.25)?
The square root is 9.5.
Explanation
To find the square root, we calculate the sum of 81 + 9.25. 81 + 9.25 = 90.25, and then √90.25 = 9.5.
Therefore, the square root of (81 + 9.25) is ±9.5.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √90.25 units and the width ‘w’ is 10 units.
We find the perimeter of the rectangle as 39 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√90.25 + 10)
= 2 × (9.5 + 10)
= 2 × 19.5 = 39 units.
FAQ on Square Root of 90.25
1.What is √90.25 in its simplest form?
2.Mention the factors of 90.25.
3.Calculate the square of 9.5.
4.Is 90.25 a prime number?
5.90.25 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 90.25?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 90.25?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 90.25
- Square root: A square root is the inverse of a square. Example: 9.5^2 = 90.25 and the inverse of the square is the square root, that is √90.25 = 9.5.
- Rational number: A rational number can be written in the form of p/q, where p and q are integers and q ≠ 0.
- Perfect square: A number that is the square of an integer is a perfect square. Example: 90.25 is a perfect square because it is 9.52
- Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. Example: 9.5 is a decimal.
- Principal square root: A number has both positive and negative square roots; however, the positive square root is often used in real-world applications and is known as the principal square root.
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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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