Question

Evaluate the following:
(i) ${\left\{(5^2+{12}^2{)}^{1/2}\right\}}^3$
(ii) ${\left\{(6^2+8^2{)}^{1/2}\right\}}^3$

Answer 1

(i)
To evaluate the value of the given expression, we can proceed as follows:

$$\begin{gathered} {\left\{{\left(5^2+{12}^2\right)}^{1/2}\right\}}^3 \\ ={\left\{{\left(25+144\right)}^{1/2}\right\}}^3 \\ ={\left\{{\left(169\right)}^{1/2}\right\}}^3 \\ ={\left\{\sqrt{\left(169\right)}\right\}}^3 \\ ={\left\{\sqrt{13\times 13}\right\}}^3 \\ ={\left\{13\right\}}^3 \\ =13\times 13\times 13=2197 \end{gathered}$$

(ii)
To evaluate the value of the given expression, we can proceed as follows:

$$\begin{gathered} {\left\{{\left(6^2+8^2\right)}^{1/2}\right\}}^3 \\ ={\left\{{\left(36+64\right)}^{1/2}\right\}}^3 \\ ={\left\{{\left(100\right)}^{1/2}\right\}}^3 \\ ={\left\{\sqrt{\left(100\right)}\right\}}^3 \\ ={\left\{\sqrt{10\times 10}\right\}}^3 \\ ={\left\{10\right\}}^3=10\times 10\times 10=1000 \end{gathered}$$