Solve -4sqrt{27}*(-3sqrt{1/3})

$$- 4 \sqrt { 27 } \times ( - 3 \sqrt { \frac { 1 } { 3 } } )$$

Evaluate

$$36$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$-4\times 3\sqrt{3}\left(-3\right)\sqrt{\frac{1}{3}}$$

Multiply -4 and 3 to get -12.

$$-12\sqrt{3}\left(-3\right)\sqrt{\frac{1}{3}}$$

Multiply -12 and -3 to get 36.

$$36\sqrt{3}\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$36\sqrt{3}\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$36\sqrt{3}\times \frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$36\sqrt{3}\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$36\sqrt{3}\times \frac{\sqrt{3}}{3}$$

Cancel out 3, the greatest common factor in 36 and 3.

$$12\sqrt{3}\sqrt{3}$$

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

$$12\times 3$$

Multiply 12 and 3 to get 36.

$$36$$

Factor

$$2^{2}\times 3^{2}$$