What is the value of 5th root of 243?

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Solution

5th root of 243 means $(243)^{\frac{1}{5}}$
We know $243 = 81 \times 3$
$243 = 3 \times 3 \times 3 \times 3 \times 3$
$(243)^{\frac{1}{5}} = (3 \times 3 \times 3 \times 3 \times 3)^{\frac{1}{5}}$
$(243)^{\frac{1}{5}} = (3^{5})^{\frac{1}{5}}$
$(243)^{\frac{1}{5}} = (3)^{5 \times \frac{1}{5}}$
$(243)^{\frac{1}{5}} = 3$

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