square root of 3 plus square root of 4 all over square root of 3 plus square root of 8
You asked:
Evaluate the expression: \(\frac{\sqrt{3 + \sqrt{4}}}{\sqrt{3 + \sqrt{8}}}\)
MathBot Answer:
\[\frac{\sqrt{3 + \sqrt{4}}}{\sqrt{3 + \sqrt{8}}} = \frac{\sqrt{5}}{\sqrt{2 \sqrt{2} + 3}}\]
\[\begin{aligned}\frac{\sqrt{3 + \sqrt{4}}}{\sqrt{3 + \sqrt{8}}}& = \sqrt{3 + \sqrt{4}} \cdot \frac{1}{\sqrt{3 + \sqrt{8}}}\\& = \sqrt{3 + 2} \cdot \frac{1}{\sqrt{3 + \sqrt{8}}}\\& = \sqrt{5} \cdot \frac{1}{\sqrt{3 + \sqrt{8}}}\\& = \sqrt{5} \cdot \frac{1}{\sqrt{3 + 2 \cdot \sqrt{2}}}\end{aligned}\]