Solve frac{sqrt{8}+sqrt{18}}{sqrt{2}}

$$\frac { \sqrt { 8 } + \sqrt { 18 } } { \sqrt { 2 } }$$

Evaluate

$$5$$

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}.

$$\frac{2\sqrt{2}+\sqrt{18}}{\sqrt{2}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Combine 2\sqrt{2} and 3\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

$$5$$