solve this

Question:

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

(a) 2

(b) $\sqrt{2}$

(c) $2 \sqrt{2}$

(d) $4 \sqrt{2}$

 

Solution:

$\sqrt[3]{2} \times \sqrt[4]{2} \times \sqrt[12]{32}=(2)^{\frac{1}{3}} \times(2)^{\frac{1}{4}} \times(32)^{\frac{1}{12}}$

$=(2)^{\frac{1}{3}} \times(2)^{\frac{1}{4}} \times\left(2^{5}\right)^{\frac{1}{12}}$

$=(2)^{\frac{1}{3}} \times(2)^{\frac{1}{4}} \times(2)^{\frac{5}{12}}$

$=(2)^{\frac{1}{3}+\frac{1}{4}+\frac{5}{12}}$

$=(2)^{\frac{4+3+5}{12}}$

$=(2)^{\frac{12}{12}}$

$=2$

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

Hence, the correct option is (a).

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