Question

what is the value of √32+ √48/√27+√18​

Answer 1

Step-by-step explanation:

$\frac{ \sqrt{32} + \sqrt{48} }{ \sqrt{27} + \sqrt{18} }$

$= \frac{ \sqrt{2 \times 2 \times 2 \times 2 \times 2} + \sqrt{2 \times 2 \times 2 \times 2 \times 3} }{ \sqrt{3 \times 3 \times 3} + \sqrt{2 \times 3 \times 3} }$

$= \frac{2 \times 2 \sqrt{2} + 2 \times 2 \sqrt{3} }{3 \sqrt{3} + 3 \sqrt{2} }$

$= \frac{4 \sqrt{2} + 4 \sqrt{3} }{3( \sqrt{3} + \sqrt{2} ) }$

$= \frac{4( \sqrt{2 } + \sqrt{3)} }{3( \sqrt{3} + \sqrt{2}) }$

$= \frac{4}{3}$