Solve sqrt{27}(sqrt{3}-sqrt{2})-5sqrt{6}

$$\sqrt { 27 } ( \sqrt { 3 } - \sqrt { 2 } ) - 5 \sqrt { 6 }$$

Evaluate

$$9-8\sqrt{6}\approx -10.595917942$$

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}.

$$3\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)-5\sqrt{6}$$

Use the distributive property to multiply 3\sqrt{3} by \sqrt{3}-\sqrt{2}.

$$3\left(\sqrt{3}\right)^{2}-3\sqrt{3}\sqrt{2}-5\sqrt{6}$$

The square of \sqrt{3} is 3.

$$3\times 3-3\sqrt{3}\sqrt{2}-5\sqrt{6}$$

Multiply 3 and 3 to get 9.

$$9-3\sqrt{3}\sqrt{2}-5\sqrt{6}$$

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

$$9-3\sqrt{6}-5\sqrt{6}$$

Combine -3\sqrt{6} and -5\sqrt{6} to get -8\sqrt{6}.

$$9-8\sqrt{6}$$