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

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

Evaluate

$$3\sqrt{2}-5\sqrt{30}\approx -23.143487188$$

Solution Steps

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

$$-5\sqrt{3}\sqrt{10}+\sqrt{3}\sqrt{6}$$

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

$$-5\sqrt{30}+\sqrt{3}\sqrt{6}$$

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}.

$$-5\sqrt{30}+\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$-5\sqrt{30}+3\sqrt{2}$$