((12^2+5^2)^.5)^3

asked by guest
on Nov 16, 2024 at 11:38 pm



You asked:

Evaluate the expression: \({{\left( {12}^{2} + {5}^{2} \right)}^{.5}}^{3}\)

MathBot Answer:

\[{{\left( {12}^{2} + {5}^{2} \right)}^{.5}}^{3} = 2197\]


\[\begin{aligned}{{\left( {12}^{2} + {5}^{2} \right)}^{.5}}^{3}& = \left(\left(12^{2} + 5^{2}\right)^{\frac{5}{10}}\right)^{3}\\& = \left(\left(144 + 5^{2}\right)^{\frac{5}{10}}\right)^{3}\\& = \left(\left(144 + 25\right)^{\frac{5}{10}}\right)^{3}\\& = \left(169^{\frac{5}{10}}\right)^{3}\\& = \left(\sqrt{169}\right)^{3}\\& = 13^{3}\\& = 2197\end{aligned}\]