Question

Simplify root 24 by 8 + root 54 by 9

Answer 1

root 24/8+root54/9
=2root6/8+3root6/9
=root6/4+root6/3
=(3root6+4root6)/12
={root6 (3+4)}/12
={root6 (7)}/12
Divide numerator as well as denominator by root6
=(root6 (7 )×root6)/(12×root6)
=42/12root6
=7/2root6

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

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

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

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

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

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

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

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