Solve 3sqrt{96}-2sqrt{150}+sqrt{24}=

$$3 \sqrt { 96 } - 2 \sqrt { 150 } + \sqrt { 24 } =$$

Evaluate

$$4\sqrt{6}\approx 9.797958971$$

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}.

$$3\times 4\sqrt{6}-2\sqrt{150}+\sqrt{24}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{6}-2\sqrt{150}+\sqrt{24}$$

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}.

$$12\sqrt{6}-2\times 5\sqrt{6}+\sqrt{24}$$

Multiply -2 and 5 to get -10.

$$12\sqrt{6}-10\sqrt{6}+\sqrt{24}$$

Combine 12\sqrt{6} and -10\sqrt{6} to get 2\sqrt{6}.

$$2\sqrt{6}+\sqrt{24}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$2\sqrt{6}+2\sqrt{6}$$

Combine 2\sqrt{6} and 2\sqrt{6} to get 4\sqrt{6}.

$$4\sqrt{6}$$