Question

evaluate the following:

[(6²+8²)^1/2]³

[(10²+24²)³]^1/2

Answer 1

$$\begin{gathered} \left(1\right). \\ {\left[{\left(6^2+8^2\right)}^{1/2}\right]}^3 \\ ={\left[{\left(36+64\right)}^{1/2}\right]}^3 \\ ={\left[{\left(100\right)}^{1/2}\right]}^3 \\ ={\left(10\right)}^3=1000 \\ \left(2\right). \\ {\left[{\left\{{\left(10\right)}^2+{\left(24\right)}^2\right\}}^3\right]}^{1/2} \\ ={\left[{\left\{{\left(10\right)}^2+{\left(24\right)}^2\right\}}^{1/2}\right]}^3 \\ ={\left[{\left(100+576\right)}^{1/2}\right]}^3 \\ ={\left[{\left(676\right)}^{1/2}\right]}^3 \\ ={\left(26\right)}^3=17576 \end{gathered}$$