Solve frac{sqrt{2}+sqrt{32}}{sqrt{2}}

$$\frac { \sqrt { 2 } + \sqrt { 32 } } { \sqrt { 2 } }$$

Evaluate

$$5$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{\sqrt{2}+4\sqrt{2}}{\sqrt{2}}$$

Combine \sqrt{2} and 4\sqrt{2} to get 5\sqrt{2}.

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

Rationalize the denominator of \frac{5\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{2}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{5\times 2}{2}$$

Multiply 5 and 2 to get 10.

$$\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$5$$

Factor

$$5$$