102 LearnersLast updated on May 26th, 2025
Square Root of 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.
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.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √2025 = 45, there is also -45, which should not be forgotten.
Square Root of 2025 Examples
Problem 1
Can you help Max find the perimeter of a square box if its side length is given as √2025?
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.
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?
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.
Problem 3
Calculate √2025 x 5.
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.
Problem 4
What will be the square root of (2025 + 0)?
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.
Problem 5
Find the area of a rectangle if its length ‘l’ is √2025 units and the width ‘w’ is 50 units.
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.
FAQ on Square Root of 2025
1.What is √2025 in its simplest form?
2.Mention the factors of 2025.
3.Calculate the square of 2025.
4.Is 2025 a prime number?
5.2025 is divisible by?
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.
