Solve 2sqrt{96}+sqrt{150}-5sqrt{54}

$$2 \sqrt { 96 } + \sqrt { 150 } - 5 \sqrt { 54 }$$

Evaluate

$$-2\sqrt{6}\approx -4.898979486$$

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}.

$$2\times 4\sqrt{6}+\sqrt{150}-5\sqrt{54}$$

Multiply 2 and 4 to get 8.

$$8\sqrt{6}+\sqrt{150}-5\sqrt{54}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$8\sqrt{6}+5\sqrt{6}-5\sqrt{54}$$

Combine 8\sqrt{6} and 5\sqrt{6} to get 13\sqrt{6}.

$$13\sqrt{6}-5\sqrt{54}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$13\sqrt{6}-5\times 3\sqrt{6}$$

Multiply -5 and 3 to get -15.

$$13\sqrt{6}-15\sqrt{6}$$

Combine 13\sqrt{6} and -15\sqrt{6} to get -2\sqrt{6}.

$$-2\sqrt{6}$$