Solve 12/sqrt{2}+sqrt{18}

$$\frac { 12 } { \sqrt { 2 } } + \sqrt { 18 }$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

Solution Steps

Rationalize the denominator of \frac{12}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{12\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt{18}$$

The square of \sqrt{2} is 2.

$$\frac{12\sqrt{2}}{2}+\sqrt{18}$$

Divide 12\sqrt{2} by 2 to get 6\sqrt{2}.

$$6\sqrt{2}+\sqrt{18}$$

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}.

$$6\sqrt{2}+3\sqrt{2}$$

Combine 6\sqrt{2} and 3\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}$$