Solve frac{6sqrt{5}}{sqrt{30}}+sqrt{150}=

$$\frac { 6 \sqrt { 5 } } { \sqrt { 30 } } + \sqrt { 150 } =$$

Evaluate

$$6\sqrt{6}\approx 14.696938457$$

Solution Steps

Rationalize the denominator of \frac{6\sqrt{5}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{6\sqrt{5}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}+\sqrt{150}$$

The square of \sqrt{30} is 30.

$$\frac{6\sqrt{5}\sqrt{30}}{30}+\sqrt{150}$$

Factor 30=5\times 6. Rewrite the square root of the product \sqrt{5\times 6} as the product of square roots \sqrt{5}\sqrt{6}.

$$\frac{6\sqrt{5}\sqrt{5}\sqrt{6}}{30}+\sqrt{150}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{6\times 5\sqrt{6}}{30}+\sqrt{150}$$

Multiply 6 and 5 to get 30.

$$\frac{30\sqrt{6}}{30}+\sqrt{150}$$

Cancel out 30 and 30.

$$\sqrt{6}+\sqrt{150}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$\sqrt{6}+5\sqrt{6}$$

Combine \sqrt{6} and 5\sqrt{6} to get 6\sqrt{6}.

$$6\sqrt{6}$$