Evaluate the following:
(i) $\left\{\left(5^{2}+12^{2}\right)^{1 / 2}\right\}^{3}$
(ii) $\left\{\left(6^{2}+8^{2}\right)^{1 / 2}\right\}^{3}$
(i)
To evaluate the value of the given expression, we can proceed as follows:
$\left\{\left(5^{2}+12^{2}\right)^{1 / 2}\right\}^{3}$
$=\left\{(25+144)^{1 / 2}\right\}^{3}$
$=\left\{(169)^{1 / 2}\right\}^{3}$
$=\{\sqrt{(169)}\}^{3}$
$=\{\sqrt{13 \times 13}\}^{3}$
$=\{13\}^{3}$
$=13 \times 13 \times 13=2197$
(ii)
To evaluate the value of the given expression, we can proceed as follows:
$\left\{\left(6^{2}+8^{2}\right)^{1 / 2}\right\}^{3}$
$=\left\{(36+64)^{1 / 2}\right\}^{3}$
$=\left\{(100)^{1 / 2}\right\}^{3}$
$=\{\sqrt{(100)}\}^{3}$
$=\{\sqrt{10 \times 10}\}^{3}$
$=\{10\}^{3}=10 \times 10 \times 10=1000$
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