Solve -4sqrt{96}-5sqrt{6}+4sqrt{5}

$$- 4 \sqrt { 96 } - 5 \sqrt { 6 } + 4 \sqrt { 5 }$$

Evaluate

$$4\sqrt{5}-21\sqrt{6}\approx -42.495012688$$

Solution Steps

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$-4\times 4\sqrt{6}-5\sqrt{6}+4\sqrt{5}$$

Multiply -4 and 4 to get -16.

$$-16\sqrt{6}-5\sqrt{6}+4\sqrt{5}$$

Combine -16\sqrt{6} and -5\sqrt{6} to get -21\sqrt{6}.

$$-21\sqrt{6}+4\sqrt{5}$$