Question

Square root 24 /8 +square root 54 / 9

Answer 1

Given 
$\sqrt{ \frac{24}{8}} + \sqrt{ \frac{54}{9} }$

$\sqrt{3} + \sqrt{6}$

$\sqrt{3} + \sqrt{2*3}$

$\sqrt{3} + \sqrt{2}* \sqrt{3}$

$\sqrt{3} [1 + \sqrt{2}]$

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\sf{ \frac{ \sqrt{24} }{8} + \frac{ \sqrt{54} }{9} }$

$\sf{ = \frac{ \sqrt{4 \times 6} }{8} + \frac{ \sqrt{9 \times 6} }{9} }$

$\sf{ = \frac{ \sqrt{6} }{4} + \frac{ \sqrt{6} }{3} }$

$\sf{ = \sqrt{6} \bigg( \frac{1}{4} + \frac{1}{3} \bigg) }$

$\textsf{Take the LCM of denominator 3 and 4 is 12.}$

$\sf{ = \sqrt{6} \bigg( \frac{3 + 4}{12} \bigg)}$

$\sf{ = \frac{7 \sqrt{6} }{12} } \: \: \bf{Ans.}$