Question

simplify root 162 + root 108 /root 72 + root 48

Answer 1

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Answer 2

Answer:

$\frac{\sqrt{162}+\sqrt{108}}{\sqrt{72}+\sqrt{48}}=\frac{3}{2}$

Step-by-step explanation:

162= 9×9×2

108 =6×6×3

72 = 6×6×2

48=4×4×3

$\sqrt{162}\\=\sqrt{9\times 9\times 2}\\=9\sqrt{2}$

$\sqrt{108}\\=\sqrt{6\times 6\times 3}\\=6\sqrt{3}$

$\sqrt{72}\\=\sqrt{6\times 6\times 2}\\=6\sqrt{2}$

$\sqrt{48}\\=\sqrt{4\times 4\times 3}\\=4\sqrt{3}$

$Now,\\\frac{\sqrt{162}+\sqrt{108}}{\sqrt{72}+\sqrt{48}}\\=\frac{9\sqrt{2}+6\sqrt{3}}{6\sqrt{2}+4\sqrt{3}}\\=\frac{3(3\sqrt{2}+2\sqrt{3})}{2(3\sqrt{2}+2\sqrt{3})}\\=\frac{3}{2}$

Therefore,

$\frac{\sqrt{162}+\sqrt{108}}{\sqrt{72}+\sqrt{48}}=\frac{3}{2}$

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