Square Root of 12.25
2026-02-28 11:48 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 like vehicle design, finance, etc. Here, we will discuss the square root of 12.25.

What is the Square Root of 12.25?

The square root is the inverse of the square of the number. 12.25 is a perfect square. The square root of 12.25 is expressed in both radical and exponential form. In radical form, it is expressed as √12.25, whereas (12.25)^(1/2) in exponential form. √12.25 = 3.5, 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 12.25

The prime factorization method is used for perfect square numbers. For non-perfect square numbers, methods like the long division method and approximation method are used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 12.25 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 12.25 is broken down into its prime factors.

Step 1: Recognize 12.25 as 1225/100.

Step 2: Find the prime factors of 1225 and 100. 1225 = 5 x 5 x 7 x 7, and 100 = 2 x 2 x 5 x 5.

Step 3: Taking the square root, √12.25 = √(1225/100) = (5 x 7) / (2 x 5) = 7/2 = 3.5.

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Square Root of 12.25 by Long Division Method

The long division method is particularly useful for non-perfect square numbers, but it can also be used to understand perfect squares. Let us now learn how to find the square root using the long division method, step by step.

Step 1: Group the numbers from right to left. For 12.25, consider 1225.

Step 2: Find n whose square is closest to 12. We can say n is 3 because 3 x 3 = 9, which is less than 12.

Step 3: Bring down the next pair (25) to make it 325. Double the current quotient (3), making it 6, and use it to find the next digit.

Step 4: Estimate the next digit (5) such that 65 x 5 = 325.

Step 5: The quotient is 3.5, which is the square root of 12.25.

Square Root of 12.25 by Approximation Method

The approximation method is another method for finding square roots and is an easy method to find the square root of a given number. Now let us learn how to find the square root of 12.25 using the approximation method.

Step 1: Find two perfect squares between which 12.25 lies. It is between 9 and 16.

Step 2: Since 12.25 is closer to 16, approximate starting from √16 = 4. Decrease gradually to find the precise value.

Step 3: Using the approximation, √12.25 is exactly 3.5.

Common Mistakes and How to Avoid Them in the Square Root of 12.25

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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √12.25?

Okay, lets begin

The area of the square is 12.25 square units.

Explanation

The area of the square = side².

The side length is given as √12.25.

Area of the square = side² = √12.25 x √12.25 = 3.5 × 3.5 = 12.25.

Therefore, the area of the square box is 12.25 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 12.25 square feet is built; if each of the sides is √12.25, what will be the square feet of half of the building?

Okay, lets begin

6.125 square feet.

Explanation

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

Dividing 12.25 by 2, we get 6.125.

So half of the building measures 6.125 square feet.

Well explained 👍

Problem 3

Calculate √12.25 x 5.

Okay, lets begin

17.5

Explanation

The first step is to find the square root of 12.25, which is 3.5.

The second step is to multiply 3.5 with 5. So 3.5 x 5 = 17.5.

Well explained 👍

Problem 4

What will be the square root of (9 + 3.25)?

Okay, lets begin

The square root is 3.5.

Explanation

To find the square root, we need to find the sum of (9 + 3.25). 9 + 3.25 = 12.25, and then √12.25 = 3.5.

Therefore, the square root of (9 + 3.25) is ±3.5.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √12.25 units and the width ‘w’ is 5 units.

Okay, lets begin

We find the perimeter of the rectangle as 17 units.

Explanation

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

Perimeter = 2 × (√12.25 + 5) = 2 × (3.5 + 5) = 2 × 8.5 = 17 units.

Well explained 👍

FAQ on Square Root of 12.25

1.What is √12.25 in its simplest form?

The prime factorization of 12.25 is 5 x 5 x 7 x 7, so the simplest form of √12.25 = 3.5.

2.Mention the factors of 12.25.

Factors of 12.25 when expressed as a fraction are 1, 2.5, 3.5, 5, 7, and 12.25.

3.Calculate the square of 12.25.

We get the square of 12.25 by multiplying the number by itself, that is 12.25 x 12.25 = 150.0625.

4.Is 12.25 a prime number?

12.25 is not a prime number. It is a perfect square of a rational number.

5.12.25 is divisible by?

12.25 is divisible by 1, 2.5, 3.5, 5, and 7.

Important Glossaries for the Square Root of 12.25

  • Square root: A square root is the inverse of a square. Example: 3.5² = 12.25, and the inverse of the square is the square root, that is √12.25 = 3.5.
     
  • Rational number: A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers.
     
  • Perfect square: A number that is the square of an integer or a rational number. Example: 12.25 is a perfect square because it is 3.5².
     
  • Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 3.5, 7.86, and 9.42 are decimals.
     
  • Quotient: The result obtained by dividing one quantity by another. For example, in 12.25 ÷ 3.5 = 3.5, the quotient is 3.5.

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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.