Question

By splitting into prime factors , find the square root of : 11025 with steps!​

Answer 1

Hi dude✌..........

Square Root of a Perfect Square by using the Prime Factorization Method

• 484 = 2 × 2 × 11 × 11. √484 = √(2 × 2 × 11 × 11) ...
• 324 = 2 × 2 × 3 × 3 × 3 × 3. √324 = √(2 × 2 × 3 × 3 × 3 × 3) ...
• 1764 = 2 x 2 x 3 x 3 x 7 x 7. ...
• 4356 = 2 x 2 x 3 x 3 x 11 x 11. ...
• 11025 = 5 x 5 x 3 x 3 x 7 x 7. ...
• = 5 × 5 × 3 × 3 × 3 × 3..........

Answer 2

Here it is given that,

We have to find the square root of the given number,

In order to do that first, we need to find the prime factors of the numbers,

The process of factoring a number in terms of prime numbers is known as prime factorization.

As we have,

The given number $11025$

Now, by prime factorization method:

=> $11025$ = 3 × 3 × 5 × 5 × 7 × 7

=> $11025$ = $(3 \times 5\times 7)^2$

Hence the square root of $11025$ is $105$.