Solve sqrt{6}(5sqrt{10}-8)

$$\sqrt { 6 } ( 5 \sqrt { 10 } - 8 )$$

Evaluate

$$\sqrt{6}\left(5\sqrt{10}-8\right)\approx 19.13391552$$

Solution Steps

Use the distributive property to multiply \sqrt{6} by 5\sqrt{10}-8.

$$5\sqrt{6}\sqrt{10}-8\sqrt{6}$$

To multiply \sqrt{6} and \sqrt{10}, multiply the numbers under the square root.

$$5\sqrt{60}-8\sqrt{6}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$5\times 2\sqrt{15}-8\sqrt{6}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{15}-8\sqrt{6}$$