Solve frac{sqrt{96}+3sqrt{3}}{sqrt{2}}=

$$\frac { \sqrt { 96 } + 3 \sqrt { 3 } } { \sqrt { 2 } } =$$

Evaluate

$$\frac{\sqrt{3}\left(3\sqrt{2}+8\right)}{2}\approx 10.602437844$$

Solution Steps

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$\frac{4\sqrt{6}+3\sqrt{3}}{\sqrt{2}}$$

Rationalize the denominator of \frac{4\sqrt{6}+3\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(4\sqrt{6}+3\sqrt{3}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(4\sqrt{6}+3\sqrt{3}\right)\sqrt{2}}{2}$$

Use the distributive property to multiply 4\sqrt{6}+3\sqrt{3} by \sqrt{2}.

$$\frac{4\sqrt{6}\sqrt{2}+3\sqrt{3}\sqrt{2}}{2}$$

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}.

$$\frac{4\sqrt{2}\sqrt{3}\sqrt{2}+3\sqrt{3}\sqrt{2}}{2}$$

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

$$\frac{4\times 2\sqrt{3}+3\sqrt{3}\sqrt{2}}{2}$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{3}+3\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{8\sqrt{3}+3\sqrt{6}}{2}$$