√5²×√7²+√12²=?
You asked:
Evaluate the expression: \({\sqrt{5}}^{2} \cdot {\sqrt{7}}^{2} + {\sqrt{12}}^{2}\)
MathBot Answer:
\[{\sqrt{5}}^{2} \cdot {\sqrt{7}}^{2} + {\sqrt{12}}^{2} = 47\]
\[\begin{aligned}{\sqrt{5}}^{2} \cdot {\sqrt{7}}^{2} + {\sqrt{12}}^{2}& = \left(\sqrt{5}\right)^{2} \cdot \left(\sqrt{7}\right)^{2} + \left(\sqrt{12}\right)^{2}\\& = 5 \cdot \left(\sqrt{7}\right)^{2} + \left(\sqrt{12}\right)^{2}\\& = 5 \cdot 7 + \left(\sqrt{12}\right)^{2}\\& = 35 + \left(\sqrt{12}\right)^{2}\\& = 35 + \left(2 \cdot \sqrt{3}\right)^{2}\\& = 35 + 12\\& = 47\end{aligned}\]