Square Root of Numbers in the Decimal Form is finding the Square Root of given Decimal numbers. We can use the prime factorization method or long division method to find out the Square Root of a Decimal. Choose the best method and know the procedure, then find the Square Root of a Decimal number. We have given all concepts of Square root on our website along with examples.

## How to find the Square Root of a Decimal?

Let us have a look at the procedure to find out the Square Root of a Decimal. Following the simple steps listed below, you can find the square root of a decimal easily. They are along the lines

1. Make the number of decimal places even by placing a zero on the extreme right of the decimal part.

2. Coming to an integral part, keep the periods as done while finding the square root of a perfect square of some natural number.

3. In the given decimal part, keep the periods on every pair of digits those starts with the first decimal place.

4. Now, find the square root of a given number.

5. Put the decimal point in the square root as soon as the integral part is exhausted.

### Finding Square Root of a Decimal Number Examples

**1. Evaluate âˆš42.25?**

Solution:

Solution:

Given the number is âˆš42.25,

To find the square root of a perfect square by the prime factorization method, we have to find the factors of 42.25.

42.25 = 6.5 Ã— 6.5

Grouping the factors into the pairs of equal factors.

(6.5 Ã— 6.5)

Take one number from each group and multiply them to find the number whose square is 42.25.

6.5.

The square root of 42.25 is 6.5.

**2. Evaluate âˆš1.96?**

Solution:

Given the number is âˆš1.96,

To find the square root of a perfect square by the prime factorization method, we have to find the factors of 1.96.

1.96 = 1.4 Ã— 1.4

Grouping the factors into the pairs of equal factors.

(1.4 Ã— 1.4)

Take one number from each group and multiply them to find the number whose square is 1.96.

1.4.

The square root of 1.96 is 1.4.

**3. Evaluate âˆš39.69?**

Solution:

Given the number is âˆš39.69,

To find the square root of a perfect square by the prime factorization method, we have to find the factors of 39.69.

39.69 = 6.3 Ã— 6.3

Grouping the factors into the pairs of equal factors.

(6.3 Ã— 6.3)

Take one number from each group and multiply them to find the number whose square is 39.69.

6.3.

The square root of 39.69 is 6.3.

**4. Evaluate âˆš547.56?**

Solution:

Given the number is âˆš547.56,

To find the square root of a perfect square by the prime factorization method, we have to find the factors of 547.56.

547.56 = 23.4 Ã— 23.4

Grouping the factors into the pairs of equal factors.

(23.4 Ã— 23.4)

Take one number from each group and multiply them to find the number whose square is 547.56.

23.4.

The square root of 547.56 is 23.4.

**5. Evaluate âˆš0.064516?**

Solution:

Given the number is âˆš0.064516,

To find the square root of a perfect square by the prime factorization method, we have to find the factors of 0.064516.

0.064516 = 0.254 Ã— 0.254

Grouping the factors into the pairs of equal factors.

(0.254 Ã— 0.254)

Take one number from each group and multiply them to find the number whose square is 0.064516.

0.254.

The square root of 0.064516 is 0.254.