Question

I need to know the answer and work

Answer 1

Answer:

$2\sqrt{17}$

Step-by-step explanation:

Given:

$\sqrt{68}$

To find:

Simplified result of the radical

Solution:

If a value is in square root and it is not a perfect square then we can solve it by finding the answer by factoring down it to smaller factors which are perfect squares and finding the square root of the smaller values

Now

68 can be written as

68 = 2 * 2 * 17

The given is

$\sqrt{68}$

It can be written as

$\sqrt{68}=\sqrt{2*2*17}$

=$\sqrt{2^{2}*17}$

Now

$\sqrt{a.b}$= $\sqrt{a}$.$\sqrt{b}$

so given become

$\sqrt{68}=\sqrt{2^{2}}*\sqrt{17}$

$\sqrt{68}=2*\sqrt{17}$                          ∵√2² = 2

$\sqrt{68}=2\sqrt{17}$                  ∵a*√b=a√b