Question

Simplify square root of 88. Explain ur reasoning.

Answer 1

The square root of 88 is $2\sqrt{22}$

Working:

As prime factorization of 88 is = 2³*11

here, 88 divides by 2, it becomes= 2*44

44 divides by 2 = 2*22, so 88 becomes 2*2*22

22 divides by 2 = 2*11, so 88 becomes 2*2*2*11

This gives us 2³*11

now, square root of this is:

$\sqrt{2*2*2*11}$

= $\sqrt{2^{2}} *\sqrt{2*11}$

As, $\sqrt{2^{2}}$=2

Final solution becomes:

$2\sqrt{2*11}$

= $2\sqrt{22}$