Question

simplify
$\frac{ \sqrt{24} }{8} + \frac{ \sqrt{54} }{9}$
​

Answer 1

Answer:

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

$\frac{ \sqrt{2 \times 2 \times 2 \times 3} }{8} + \frac{ \sqrt{3 \times 3 \times 2 \times 3} }{9}$

$\frac{2 \sqrt{6} }{8} + \frac{3 \sqrt{6} }{9}$

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

Take L.C.M of 4 and 3

$\frac{3 \sqrt{6} + 4 \sqrt{6} }{12}$

$\frac{7 \sqrt{6} }{12}$

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Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

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

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

$\sf{ = \frac{2 \sqrt{6} }{8} + \frac{3 \sqrt{6} }{9} }$

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

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

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

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