Solve (3sqrt{6}+sqrt{30})divsqrt{6}

$$(3 \sqrt{ 6 } + \sqrt{ 30 } ) \div \sqrt{ 6 }$$

Evaluate

$$\sqrt{5}+3\approx 5.236067977$$

Solution Steps

Rationalize the denominator of \frac{3\sqrt{6}+\sqrt{30}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\left(3\sqrt{6}+\sqrt{30}\right)\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\left(3\sqrt{6}+\sqrt{30}\right)\sqrt{6}}{6}$$

Use the distributive property to multiply 3\sqrt{6}+\sqrt{30} by \sqrt{6}.

$$\frac{3\left(\sqrt{6}\right)^{2}+\sqrt{30}\sqrt{6}}{6}$$

The square of \sqrt{6} is 6.

$$\frac{3\times 6+\sqrt{30}\sqrt{6}}{6}$$

Multiply 3 and 6 to get 18.

$$\frac{18+\sqrt{30}\sqrt{6}}{6}$$

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

$$\frac{18+\sqrt{6}\sqrt{5}\sqrt{6}}{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{18+6\sqrt{5}}{6}$$

Divide each term of 18+6\sqrt{5} by 6 to get 3+\sqrt{5}.

$$3+\sqrt{5}$$