Question

Simplify : Square root of 72 + square root of 800 + square root of 18

Answer 1

Answer with complete explanation
$\sqrt{72} + \sqrt{800} + \sqrt{18}$
$= \sqrt{2^{3} * 3^{2}} + \sqrt{800} + \sqrt{18}$
$= \sqrt{ 2^{2} * 2 * 3^{2} } + \sqrt{800} + \sqrt{18}$
$= \sqrt{2} \sqrt{ 2^{2} } \sqrt{ 3^{2} } + \sqrt{800} + \sqrt{18}$
$= 2 \sqrt{2} \sqrt{ 3^{2} } + \sqrt{800} + \sqrt{18}$
$= 2*3* \sqrt{2} + \sqrt{800} + \sqrt{18}$
$= 6 \sqrt{2} + \sqrt{800} + \sqrt{18}$
$= 6 \sqrt{2} + \sqrt{2^{5} * 5^{2} } + \sqrt{18}$
$= 6 \sqrt{2} + \sqrt{ 2^{4} * 2 * 5^{2} } + \sqrt{18}$
$= 6 \sqrt{2} + \sqrt{2} \sqrt{ 2^{4} } \sqrt{ 5^{2} } + \sqrt{18}$
$= 6 \sqrt{2} + 2^{2} \sqrt{2} \sqrt{5^{2} } + \sqrt{18}$
$= 6 \sqrt{2} + 4*5* \sqrt{2} + \sqrt{18}$
$= 6 \sqrt{2} + 20 \sqrt{2} + \sqrt{18}$
$= 6 \sqrt{2} + 20 \sqrt{2} + \sqrt{2 * 3^{2} }$
$= 6 \sqrt{2} + 20 \sqrt{2} + \sqrt{2} \sqrt{ 3^{2} }$
$= 6 \sqrt{2} + 20 \sqrt{2} + 3 \sqrt{2}$
$= (6+20+3) \sqrt{2}$
$= 29 \sqrt{2}$
Sorry for the lengthy answer. My purpose was that you should understand the answer. 

Hope this may help you.