Solve 4sqrt{27}-6sqrt{1/3}

$$4 \sqrt { 27 } - 6 \sqrt { \frac { 1 } { 3 } }$$

Evaluate

$$10\sqrt{3}\approx 17.320508076$$

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}.

$$4\times 3\sqrt{3}-6\sqrt{\frac{1}{3}}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{3}-6\sqrt{\frac{1}{3}}$$

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

$$12\sqrt{3}-6\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$12\sqrt{3}-6\times \frac{1}{\sqrt{3}}$$

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

$$12\sqrt{3}-6\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$12\sqrt{3}-6\times \frac{\sqrt{3}}{3}$$

Cancel out 3, the greatest common factor in 6 and 3.

$$12\sqrt{3}-2\sqrt{3}$$

Combine 12\sqrt{3} and -2\sqrt{3} to get 10\sqrt{3}.

$$10\sqrt{3}$$