Square Root of 9025
2026-02-28 19:16 Diff
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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 9025.

What is the Square Root of 9025?

The square root is the inverse of the square of the number. 9025 is a perfect square. The square root of 9025 is expressed in both radical and exponential form. In the radical form, it is expressed as √9025, whereas (9025)^(1/2) in the exponential form. √9025 = 95, 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 9025

The prime factorization method and the long division method can be used to find the square root of perfect square numbers like 9025. Let us now learn the following methods:

  • Prime factorization method
  • Long division method

Square Root of 9025 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 9025 is broken down into its prime factors.

Step 1: Finding the prime factors of 9025

Breaking it down, we get 5 x 5 x 19 x 19: 5^2 x 19^2

Now we found out the prime factors of 9025. The second step is to make pairs of those prime factors. Since 9025 is a perfect square, we can pair the factors (5 x 19) and take one factor from each pair to find the square root.

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Square Root of 9025 by Long Division Method

The long division method is another way to find the square root of perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, we need to group the numbers from right to left into pairs. In the case of 9025, we group it as 90 and 25.

Step 2: Now we need to find a number whose square is less than or equal to 90. We can choose 9 because 9 x 9 = 81, which is less than 90. Now the quotient is 9, and after subtracting 81 from 90, the remainder is 9.

Step 3: Bring down the next pair, 25, to make the new dividend 925. Add the old divisor 9 to itself (9 + 9 = 18), which becomes our new divisor.

Step 4: Find n such that 18n x n ≤ 925. Considering n as 5, (180 + 5) x 5 = 925.

Step 5: Subtract 925 from 925, and the remainder is 0.

So the square root of √9025 is 95.

Square Root of 9025 by Approximation Method

Approximation method is another method for finding the square roots, but since 9025 is a perfect square, we have already found its square root exactly.

Step 1: We identify the closest perfect square of √9025, which is 9025 itself. Since 9025 is already a perfect square, the approximation is not needed, and √9025 = 95.

Common Mistakes and How to Avoid Them in the Square Root of 9025

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes that students tend to make in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √9025?

Okay, lets begin

The area of the square is 9025 square units.

Explanation

The area of the square = side^2.

The side length is given as √9025.

Area of the square = side^2 = √9025 x √9025 = 95 x 95 = 9025

Therefore, the area of the square box is 9025 square units.

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Problem 2

A square-shaped garden measuring 9025 square feet is built; if each of the sides is √9025, what will be the square feet of half of the garden?

Okay, lets begin

4512.5 square feet

Explanation

We can just divide the given area by 2 as the garden is square-shaped.

Dividing 9025 by 2 = we get 4512.5

So half of the garden measures 4512.5 square feet.

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Problem 3

Calculate √9025 x 5.

Okay, lets begin

475

Explanation

The first step is to find the square root of 9025, which is 95.

The second step is to multiply 95 with 5.

So, 95 x 5 = 475.

Well explained 👍

Problem 4

What will be the square root of (9025 + 0)?

Okay, lets begin

The square root is 95.

Explanation

To find the square root, we need to find the sum of (9025 + 0), which is 9025.

The square root of 9025 is 95.

Therefore, the square root of (9025 + 0) is ±95.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √9025 units and the width ‘w’ is 50 units.

Okay, lets begin

The perimeter of the rectangle is 290 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√9025 + 50) = 2 × (95 + 50) = 2 × 145 = 290 units.

Well explained 👍

FAQ on Square Root of 9025

1.What is √9025 in its simplest form?

The prime factorization of 9025 is 5^2 x 19^2, so the simplest form of √9025 = √(5^2 x 19^2) = 95.

2.Mention the factors of 9025.

Factors of 9025 are 1, 5, 19, 25, 95, 361, 1805, and 9025.

3.Calculate the square of 95.

We get the square of 95 by multiplying the number by itself, that is 95 x 95 = 9025.

4.Is 9025 a prime number?

9025 is not a prime number, as it has more than two factors.

5.9025 is divisible by?

9025 is divisible by 1, 5, 19, 25, 95, 361, 1805, and 9025.

Important Glossaries for the Square Root of 9025

  • Square root: A square root is the inverse of a square. Example: 9^2 = 81, and the inverse of the square is the square root, that is, √81 = 9.
     
  • 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 perfect square is a number that is the square of an integer. For example: 9025 is a perfect square because it is 95^2.
     
  • Prime factorization: The expression of a number as a product of prime numbers. For example, the prime factorization of 9025 is 5^2 x 19^2.
     
  • Divisor: A divisor is a number that divides another number completely without leaving a remainder. For example, 5 is a divisor of 9025.

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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.