Evaluate the following: $\sqrt[3]{-1 \frac{61}{64}}$.

Given: $\sqrt[3]{-1 \frac{61}{64}}$.

To do: To evaluate: $\sqrt[3]{-1 \frac{61}{64}}$.

Solution:

$\sqrt[3]{-1 \frac{61}{64}}$

$=\sqrt[3]{\frac{-64+61}{64}}$

$=\sqrt[3]{\frac{3}{-64}}$

$=\sqrt[3]{\frac{3}{( -4)\times( -4)\times( -4)}}$

$=\frac{\sqrt[3]{3}}{-4}$

$=-\frac{\sqrt[3]{3}}{4}$

Thus, $\sqrt[3]{-1 \frac{61}{64}}=-\frac{\sqrt[3]{3}}{4}$.

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Updated on: 10-Oct-2022

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