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Q.

The simplest form of $\sqrt[4]{112}$ is $a \sqrt[4]{b},$ then $a + b$ is _________

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answer is 9.

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Detailed Solution

$\sqrt[4]{112}$ is $↕ a \sqrt[4]{b},$

$\sqrt[4]{112} = \sqrt[4]{2^{4} \times 7}$

$= \sqrt[4]{2^{4}} \sqrt[4]{7}$

$a \sqrt[4]{b} = 2 \sqrt[4]{7}$

comparing $↕ a = 2$

$b = 7$

$a + b = 2 + 7 = 9$

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