Evaluate the following:$( a).\ ( \sqrt{5^{2}+12^{2}})^{3}$
$( b).\ \sqrt[3]{-1 \frac{61}{64}}$
$( c).\ \sqrt[3]{0.001728}$$( d).\ \sqrt[3]{3375 \times(-1728)}$

Solution:

$( a).\ ( \sqrt{5^{2}+12^{2}})^{3}$

$=( \sqrt{5^2+12^2})^{3}$

$=( \sqrt{25+144})^3$

$=( \sqrt{169})^3$

$=( 13)^3$

$=13\times13\times13$

$=2197$

$( b).\ \sqrt[3]{-1\frac{61}{64}}$

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

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

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

$=-\frac{1}{4}\sqrt[3]{3}$

$( c).\ \sqrt[3]{0.001728}$

$=\sqrt[3]{0.12\times0.12\times0.12}$

$=0.12$

$( d).\ \sqrt[3]{3375 \times( -1728)}$

$=\sqrt[3]{\underline{3\times3\times3}\times\underline{5\times5\times5}\times\underline{4\times4\times4}\times\underline{( -3)\times( -3)\times( -3)}}$

$=3\times5\times4\times( -4)$

$=-240$

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Updated on: 10-Oct-2022

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