square root of 3 plus square root of 4 all over square root of 3 plus square root of 8

asked by guest
on Nov 14, 2024 at 5:44 pm



You asked:

Evaluate the expression: 3+43+8\frac{\sqrt{3 + \sqrt{4}}}{\sqrt{3 + \sqrt{8}}}

MathBot Answer:

3+43+8=522+3\frac{\sqrt{3 + \sqrt{4}}}{\sqrt{3 + \sqrt{8}}} = \frac{\sqrt{5}}{\sqrt{2 \sqrt{2} + 3}}

3+43+8=3+4⋅13+8=3+2⋅13+8=5⋅13+8=5⋅13+2⋅2\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}

+ Submit Question