Solve frac{sqrt{7}+sqrt{18}}{sqrt{2}}

$$\frac { \sqrt { 7 } + \sqrt { 18 } } { \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{14}}{2}+3\approx 4.870828693$$

Solution Steps

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}.

$$\frac{\sqrt{7}+3\sqrt{2}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{7}+3\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(\sqrt{7}+3\sqrt{2}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(\sqrt{7}+3\sqrt{2}\right)\sqrt{2}}{2}$$

Use the distributive property to multiply \sqrt{7}+3\sqrt{2} by \sqrt{2}.

$$\frac{\sqrt{7}\sqrt{2}+3\left(\sqrt{2}\right)^{2}}{2}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{14}+3\left(\sqrt{2}\right)^{2}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{14}+3\times 2}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{14}+6}{2}$$