Solve 1/sqrt{2}+sqrt{8}

$$\frac { 1 } { \sqrt { 2 } } + \sqrt { 8 }$$

Evaluate

$$\frac{5\sqrt{2}}{2}\approx 3.535533906$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt{8}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}+\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{\sqrt{2}}{2}+2\sqrt{2}$$

Combine \frac{\sqrt{2}}{2} and 2\sqrt{2} to get \frac{5}{2}\sqrt{2}.

$$\frac{5}{2}\sqrt{2}$$