Solve frac{12sqrt{2}+20}{sqrt{6}}=

$$\frac { 12 \sqrt { 2 } + 20 } { \sqrt { 6 } } =$$

Evaluate

$$\frac{2\sqrt{6}\left(3\sqrt{2}+5\right)}{3}\approx 15.09316904$$

Solution Steps

Rationalize the denominator of \frac{12\sqrt{2}+20}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\left(12\sqrt{2}+20\right)\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\left(12\sqrt{2}+20\right)\sqrt{6}}{6}$$

Use the distributive property to multiply 12\sqrt{2}+20 by \sqrt{6}.

$$\frac{12\sqrt{2}\sqrt{6}+20\sqrt{6}}{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$\frac{12\sqrt{2}\sqrt{2}\sqrt{3}+20\sqrt{6}}{6}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{12\times 2\sqrt{3}+20\sqrt{6}}{6}$$

Multiply 12 and 2 to get 24.

$$\frac{24\sqrt{3}+20\sqrt{6}}{6}$$

Factor

$$\frac{2 \sqrt{6} {(\sqrt{3} \sqrt{6} + 5)}}{3} = 15.093169039552768$$