Square Root of 90.25
2026-02-28 12:56 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-90.25

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Last updated on August 5, 2025

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: -

  1. Prime factorization method 
  2. Long division method 
  3. 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.

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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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √90.25?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √90.25 × 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (81 + 9.25)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √90.25 units and the width ‘w’ is 10 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 90.25

1.What is √90.25 in its simplest form?

√90.25 is already in its simplest form as 9.5 since 90.25 is a perfect square, represented as (9.5)^2.

2.Mention the factors of 90.25.

Factors of 90.25 are 1, 9.5, and 90.25, considering it as the square of 9.5.

3.Calculate the square of 9.5.

We get the square of 9.5 by multiplying the number by itself, that is 9.5 × 9.5 = 90.25.

4.Is 90.25 a prime number?

5.90.25 is divisible by?

90.25 is divisible by 1, 9.5, and 90.25.

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

: He loves to play the quiz with kids through algebra to make kids love it.