Worksheet on square root using prime factorization method is useful for the students to prepare well for the exams. Here to find the prime factorization of a number we will divide the number by the first even prime number and we will continue dividing until we get a decimal or a reminder after that we will divide with an odd number until the only numbers left are prime numbers and write the number as a product of prime number.

To find the square root using prime factorization first, we will resolve the number inside the square root into prime factors and then inside the square root, for every two same numbers multiplied and one number can be taken out of the square root. And in the next step, we will combine the like square root terms using mathematical operation. Here in this finding square root by prime factorization method worksheet, we will solve various types of questions to make you familiar with the concept.

1. Find the square root of the number 196 by using the method of prime factorization?

## Solution:

Given the number is 196,

the prime factorization of 196 is

196= 2×2×17×17

And the square root of 196 is 14.

2. Find the square root of the number 361 by using the method of prime factorization?

## Solution:

Given the number is 361,

the prime factorization of 361 is, as the number 361 is a composite number, so

361= 19×19

And the square root of 361 is 19.

3. Find the square root of the number 576 by using the method of prime factorization?

## Solution:

Given the number is 576,

the prime factorization of 576 is

576= 2×2×2×2×2×3×3

And the square root of 576 is 24.

4. Find the square root of the number 1849 by using the method of prime factorization?

## Solution:

Given the number is 1,849,

the prime factorization of 1,849 is

1,849= 43×43

And the square root of 1,849 is 14.

5. Find the square root of the number 2401 by using the method of prime factorization?

## Solution:

Given the number is 2,401,

the prime factorization of 2,401 is

2,401= 7×7×7×7

And the square root of 2,401 is 49.

6. Find the smallest number by which 2925 must be divided to obtain a perfect square. Also, find the square root of the perfect square so obtained?

## Solution:

Given number is 2,925

Prime factors of 2,925 are

2,925= 3×3×5×5×13

And here the new number is 13, so 2,925÷13

= 225.

and the square root of 225 is 15.

**7.** If 2,025 students are seated in the auditorium in such a way that each row contains as many students as the number of rows. Find the number of rows and the number of students in each row.

## Solution:

The number of students are 2,025

To find the number of rows, we will find the square root of 2,025

So the square root of 2,025 is 45.

And the number of rows and the number of students are 45.

**8.** The people in a community arranged a picnic. Each one contributed as many rupees as the number of people in the community. If the total contribution is Rs 1,089, find the strength of the people in the community.

## Solution:

Let the number of people in the community be X

And the contribution by each person is Rs. X

X×X= 1,089

X^2= 1,089

X= 33.

So the strength of the people in the community is 33.