MCQ
$\sqrt[6]{5} \times \sqrt[3]{2} \times \sqrt{3} \times \sqrt[12]{6}$ is equal to
- A$\sqrt[12]{1749600}$
- B$\sqrt[3]{2} \times \sqrt[12]{109350}$
- C$\sqrt[12]{177960}$
- ✓both (a) and (b)
✓
Answer
Correct option: D.
both (a) and (b)
(d)
$ \begin{array}{l} \text { }\sqrt[6]{5} \times \sqrt[3]{2} \times \sqrt{3} \times \sqrt[12]{6}=5^{1 / 6} \times 2^{1 / 3} \times 3^{1 / 2} \times 6^{1 / 12}=5^{2 / 12} \times 2^{4 / 12} \times 3^{6 / 12} \times 6^{1 / 12} \\ =\left(5^2\right)^{1 / 12} \times\left(2^4\right)^{1 / 12} \times\left(3^6\right)^{1 / 12} \times(6)^{1 / 12}=\left(5^2 \times 2^4 \times 3^6 \times 6\right)^{1 / 12} \\ =(25 \times 16 \times 729 \times 6)^{1 / 12}=(1749600)^{1 / 12}=\sqrt[12]{1749600} \\ \text { Again, } \\ \sqrt[6]{5} \times \sqrt[3]{2} \times \sqrt{3} \times \sqrt[12]{6}=\left(5^2 \times 2^4 \times 3^6 \times 6\right)^{1 / 12}=2^{4 / 12} \times\left(5^2 \times 3^6 \times 6\right)^{1 / 12}=2^{1 / 3} \times(25 \times 729 \times 6)^{1 / 12} \\ =\sqrt[3]{2} \sqrt[12]{109350} \end{array}$
$ \begin{array}{l} \text { }\sqrt[6]{5} \times \sqrt[3]{2} \times \sqrt{3} \times \sqrt[12]{6}=5^{1 / 6} \times 2^{1 / 3} \times 3^{1 / 2} \times 6^{1 / 12}=5^{2 / 12} \times 2^{4 / 12} \times 3^{6 / 12} \times 6^{1 / 12} \\ =\left(5^2\right)^{1 / 12} \times\left(2^4\right)^{1 / 12} \times\left(3^6\right)^{1 / 12} \times(6)^{1 / 12}=\left(5^2 \times 2^4 \times 3^6 \times 6\right)^{1 / 12} \\ =(25 \times 16 \times 729 \times 6)^{1 / 12}=(1749600)^{1 / 12}=\sqrt[12]{1749600} \\ \text { Again, } \\ \sqrt[6]{5} \times \sqrt[3]{2} \times \sqrt{3} \times \sqrt[12]{6}=\left(5^2 \times 2^4 \times 3^6 \times 6\right)^{1 / 12}=2^{4 / 12} \times\left(5^2 \times 3^6 \times 6\right)^{1 / 12}=2^{1 / 3} \times(25 \times 729 \times 6)^{1 / 12} \\ =\sqrt[3]{2} \sqrt[12]{109350} \end{array}$
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