how to solve 1/root 2 multiplied by root 3/2
You asked:
Evaluate the expression: \(\frac{1}{\sqrt[2]{2}} \sqrt[2]{\frac{3}{2}}\)
MathBot Answer:
\[\frac{1}{\sqrt[2]{2}} \sqrt[2]{\frac{3}{2}} = \frac{\sqrt{3}}{2} \approx 0.86602540378443864676372317075294\]
\[\begin{aligned}\frac{1}{\sqrt[2]{2}} \sqrt[2]{\frac{3}{2}}& = \frac{1}{\sqrt{2}} \cdot \sqrt{\frac{3}{2}}\\& = \frac{1}{2} \cdot \sqrt{2} \cdot \sqrt{\frac{3}{2}}\\& = \frac{1}{2} \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \sqrt{6}\\& = \frac{1}{2} \cdot \sqrt{3}\end{aligned}\]