[3] 2 [4] 2 [12] 32 =? - Vidyadip

Question

$\sqrt[3]{2}\times\sqrt[4]{2}\times\sqrt[12]{32}=?$

✓

Answer

$2$
Solution:
$\sqrt[3]{2}\times\sqrt[4]{2}\times\sqrt[12]{32}$
$=\sqrt[3]{2}\times\sqrt[4]{2}\times\sqrt[12]{2^5}$
$=2^\frac{1}{3}\times2^\frac{1}{4}\times2^{5\times\frac{1}{12}}$
$=2^{\frac{1}{3}+\frac{1}{4}+\frac{5}{12}}$
$=2^{\frac{4+3+5}{12}}$
$=2^{\frac{12}{12}}$
$=2$
Hence, the correct option is (a).

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