MCQ
The value of $\frac{\sqrt{48}+\sqrt{32}}{\sqrt{27}+\sqrt{18}},$ is:
- ✓$\frac{4}{3}$
- B$4$
- C$3$
- D$\frac{3}{4}$
✓
Answer
Correct option: A.
$\frac{4}{3}$
$\sqrt{48}=\sqrt{16\times3}=4\sqrt3$
$\sqrt{32}=\sqrt{16\times2}=4\sqrt2$
$\sqrt{27}=\sqrt{9\times3}=3\sqrt3$
$\sqrt{18}=\sqrt{9\times2}=3\sqrt2$
Now, $\frac{\sqrt{48}+\sqrt{32}}{\sqrt{27}+\sqrt{18}}=\frac{4\sqrt3+4\sqrt2}{3\sqrt3+3\sqrt2}$
$=\frac{4\big(\sqrt{\not3}+\sqrt{\not2}\big)}{3\big(\sqrt{\not3}+\sqrt{\not2}\big)}$
$=\frac{4}{3}$
Hence, correct option is $(a).$
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