Solve -(3)frac{sqrt{3}*sqrt{12}}{sqrt{2}}=

$$- ( 3 ) \frac { \sqrt { 3 } \times \sqrt { 12 } } { \sqrt { 2 } } =$$

Evaluate

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

Solution Steps

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Calculate the square root of 4 and get 2.

$$-3\times \frac{3\times 2}{\sqrt{2}}$$

Multiply 3 and 2 to get 6.

$$-3\times \frac{6}{\sqrt{2}}$$

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

$$-3\times \frac{6\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-3\times \frac{6\sqrt{2}}{2}$$

Divide 6\sqrt{2} by 2 to get 3\sqrt{2}.

$$-3\times 3\sqrt{2}$$

Multiply -3 and 3 to get -9.

$$-9\sqrt{2}$$