Question

square root of 1156 by prime factorization

Answer 1

1156 = 2 x 578 
= 2 x 2 x 289 
= 2 x 2 x 17 x 17 
∴ √1156 = √(2 x 2 x 17 x 17)
√1156 = 2 x 17 
√1156 = = 34 

Answer 2

The square root of 1156 is 34.

Solution:

Let us factorize the number 1156.

First as the last number is even we will divide number by 2 till the last number is even ,

$\frac{1156}{2} = 578$

$\frac{578}{2} = 289$

Now we know 289 is the square of 17

$\Rightarrow \frac{289}{17} = 17$

So factorizing 1156, we get $= (2\times2\times17\times17)=(2^2\times17^2)$

Hence, the square root of $1156 = (2\times17) =34$