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

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

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

Solution Steps

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}.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

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

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

$$3\sqrt{2}$$