Solve 7sqrt{6}(sqrt{10}+8)

$$7 \sqrt { 6 } ( \sqrt { 10 } + 8 )$$

Evaluate

$$7\sqrt{6}\left(\sqrt{10}+8\right)\approx 191.393192443$$

Solution Steps

Use the distributive property to multiply 7\sqrt{6} by \sqrt{10}+8.

$$7\sqrt{6}\sqrt{10}+56\sqrt{6}$$

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

$$7\sqrt{60}+56\sqrt{6}$$

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}.

$$7\times 2\sqrt{15}+56\sqrt{6}$$

Multiply 7 and 2 to get 14.

$$14\sqrt{15}+56\sqrt{6}$$