Simplify: $3 \sqrt{2}+\sqrt[4]{64}+\sqrt[4]{2500}+\sqrt[6]{8}$.

Given: $3 \sqrt{2}+\sqrt[4]{64}+\sqrt[4]{2500}+\sqrt[6]{8}$.

To do: To simplify $3 \sqrt{2}+\sqrt[4]{64}+\sqrt[4]{2500}+\sqrt[6]{8}$.

Solution:

$3 \sqrt{2}+\sqrt[4]{64}+\sqrt[4]{2500}+\sqrt[6]{8}$

$=3\sqrt{2}+\sqrt[4]{2^6}+\sqrt[4]{5^4\times4}+\sqrt[6]{2^3}$

$=3\sqrt{2}+2\sqrt[4]{4}+5\sqrt[4]{4}+\sqrt{2}$

$=3\sqrt{2}+2\sqrt{2}+5\sqrt{2}+\sqrt{2}$

$=11\sqrt{2}$

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Updated on: 10-Oct-2022

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