Solve 27*sqrt{3}(-5sqrt{10}+sqrt{6})

$$27 \cdot \sqrt { 3 } ( - 5 \sqrt { 10 } + \sqrt { 6 } )$$

Evaluate

$$81\sqrt{2}-135\sqrt{30}\approx -624.87415408$$

Solution Steps

Use the distributive property to multiply 27\sqrt{3} by -5\sqrt{10}+\sqrt{6}.

$$-135\sqrt{3}\sqrt{10}+27\sqrt{3}\sqrt{6}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$-135\sqrt{30}+27\sqrt{3}\sqrt{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$-135\sqrt{30}+27\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$-135\sqrt{30}+27\times 3\sqrt{2}$$

Multiply 27 and 3 to get 81.

$$-135\sqrt{30}+81\sqrt{2}$$