Evaluate the following:
Question:

Evaluate the following:

(i) $\left\{\left(5^{2}+12^{2}\right)^{1 / 2}\right\}^{3}$

(ii) $\left\{\left(6^{2}+8^{2}\right)^{1 / 2}\right\}^{3}$

Solution:

(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:

$\left\{\left(6^{2}+8^{2}\right)^{1 / 2}\right\}^{3}$

$=\left\{(36+64)^{1 / 2}\right\}^{3}$

$=\left\{(100)^{1 / 2}\right\}^{3}$

$=\{\sqrt{(100)}\}^{3}$

$=\{\sqrt{10 \times 10}\}^{3}$

$=\{10\}^{3}=10 \times 10 \times 10=1000$