Question

Simplify - $\sqrt[8]{5}+\sqrt{20}-\sqrt{125}$

Answer 1

▪︎■ ANSWER ■▪︎

To simplify a surd, write the number under the root sign as the product of two factors, one of which is the largest perfect square.

$\rightarrow$$\bf\underline{Solution}$

$\sqrt[8]{5} + \sqrt{20} - \sqrt{125} \\ = \sqrt[8]{5} + \sqrt{4 \times 5} - \sqrt[]{25 \times 5} \\ = \sqrt[8]{5} + \sqrt[2]{5} - \sqrt[5]{5} \\ = (8 + 2 - 5) \sqrt{5} \\ = \sqrt[5]{5}\\ \\\therefore \bf Your \: Answer \: is \: \boxed{ \sqrt[5]{5} }$

$\longrightarrow$ Note - the factor 16 is the largest perfect square. Recall that the numbers 1, 4, 9, 16, 25, 36, 49, ... are perfect squares.

Answer 2

Answer:

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