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

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

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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}.

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

Cancel out 2 and 2.

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

Combine \frac{\sqrt{2}}{2} and \sqrt{2} to get \frac{3}{2}\sqrt{2}.

$$\frac{3}{2}\sqrt{2}$$