​ The value of √48 + √32/√27 + √18 is A. 4/3 B. 4 C. 3 D. 3/4 ​

Question

The value of \(\frac{\sqrt{48}+\sqrt{32}}{\sqrt{27}+\sqrt{18}}\) is

A. \(\frac{4}{3}\)

B. 4

C. 3

D. \(\frac{3}{4}\)

Answer 1

\(\frac{\sqrt{48}+\sqrt{32}}{\sqrt{27}+\sqrt{18}}\)

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

= \(\frac{36+12\sqrt{6}-12\sqrt{6}-24}{(27-18)}\) = \(\frac{12}{9}\) = \(\frac{4}{3}\)