Square Root of 2025
2026-02-28 09:04 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 2025.

What is the Square Root of 2025?

The square root is the inverse of the square of the number. 2025 is a perfect square. The square root of 2025 is expressed in both radical and exponential form. In the radical form, it is expressed as √2025, whereas in exponential form it is expressed as (2025)^(1/2). √2025 = 45, 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 2025

The prime factorization method is used for perfect square numbers. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 2025 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 2025 is broken down into its prime factors.

Step 1: Finding the prime factors of 2025

Breaking it down, we get 3 x 3 x 3 x 3 x 5 x 5: 3^4 x 5^2

Step 2: Now we found out the prime factors of 2025. The second step is to make pairs of those prime factors. Since 2025 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating √2025 using prime factorization gives us 3^2 x 5 = 45.

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Square Root of 2025 by Long Division Method

The long division method is particularly used for both perfect and non-perfect square numbers. 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. In the case of 2025, we need to group it as 25 and 20.

Step 2: Now we need to find n whose square is 20. We can say n is ‘4’ because 4 x 4 = 16 is lesser than or equal to 20. Now the quotient is 4, and the remainder is 4 after subtracting 16 from 20.

Step 3: Now let us bring down 25, making the new dividend 425. Add the old divisor with the same number, 4 + 4, we get 8, which will be our new divisor.

Step 4: The new divisor will be 8x, and we need to find the value of x such that 8x x x ≤ 425. Considering x as 5, 85 x 5 = 425.

Step 5: Subtract 425 from 425, and the remainder is 0. Now the quotient is 45.

So the square root of √2025 is 45.

Square Root of 2025 by Approximation Method

The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 2025 using the approximation method.

Step 1: Now we have to find the closest perfect square of √2025. The closest perfect squares around 2025 are 2025 itself. √2025 is exactly 45.

Therefore, the square root of 2025 is 45.

Common Mistakes and How to Avoid Them in the Square Root of 2025

Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. 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 perimeter of a square box if its side length is given as √2025?

Okay, lets begin

The perimeter of the square is 180 units.

Explanation

The perimeter of the square is 4 times the side length.

The side length is given as √2025.

Perimeter = 4 x √2025 = 4 x 45 = 180 units.

Therefore, the perimeter of the square box is 180 units.

Well explained 👍

Problem 2

A square-shaped building measures 2025 square feet in area. If each of the sides is √2025, what will be the square footage of half of the building?

Okay, lets begin

1012.5 square feet

Explanation

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

Dividing 2025 by 2, we get 1012.5.

So, half of the building measures 1012.5 square feet.

Well explained 👍

Problem 3

Calculate √2025 x 5.

Okay, lets begin

225

Explanation

The first step is to find the square root of 2025, which is 45.

The second step is to multiply 45 by 5.

So, 45 x 5 = 225.

Well explained 👍

Problem 4

What will be the square root of (2025 + 0)?

Okay, lets begin

The square root is 45.

Explanation

To find the square root, we need to find the sum of (2025 + 0), which is 2025, and then √2025 = 45.

Therefore, the square root of (2025 + 0) is ±45.

Well explained 👍

Problem 5

Find the area of a rectangle if its length ‘l’ is √2025 units and the width ‘w’ is 50 units.

Okay, lets begin

The area of the rectangle is 2250 square units.

Explanation

Area of the rectangle = length x width

Area = √2025 x 50 = 45 x 50 = 2250 square units.

Well explained 👍

FAQ on Square Root of 2025

1.What is √2025 in its simplest form?

The prime factorization of 2025 is 3 x 3 x 3 x 3 x 5 x 5, so the simplest form of √2025 = √(3^4 x 5^2) = 3^2 x 5 = 45.

2.Mention the factors of 2025.

Factors of 2025 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, and 2025.

3.Calculate the square of 2025.

We get the square of 2025 by multiplying the number by itself, that is 2025 x 2025 = 4100625.

4.Is 2025 a prime number?

2025 is not a prime number, as it has more than two factors.

5.2025 is divisible by?

2025 has many factors; those are 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, and 2025.

Important Glossaries for the Square Root of 2025

  • Square root: A square root is the inverse of a square. Example: 6^2=36, and the inverse of the square is the square root, that is √36=6.
     
  • 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. Example: 2025 is a perfect square because it is 45^2.
     
  • Prime factorization: Prime factorization is expressing a number as the product of its prime factors.
     
  • Divisor: A divisor is a number by which another number is divided. For example, in 45 ÷ 5 = 9, the divisor is 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.

Fun Fact

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