Solve 9sqrt{24}+3sqrt{54}-12sqrt{6}=

$$9 \sqrt { 24 } + 3 \sqrt { 54 } - 12 \sqrt { 6 } =$$

Evaluate

$$15\sqrt{6}\approx 36.742346142$$

Solution Steps

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}.

$$9\times 2\sqrt{6}+3\sqrt{54}-12\sqrt{6}$$

Multiply 9 and 2 to get 18.

$$18\sqrt{6}+3\sqrt{54}-12\sqrt{6}$$

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}.

$$18\sqrt{6}+3\times 3\sqrt{6}-12\sqrt{6}$$

Multiply 3 and 3 to get 9.

$$18\sqrt{6}+9\sqrt{6}-12\sqrt{6}$$

Combine 18\sqrt{6} and 9\sqrt{6} to get 27\sqrt{6}.

$$27\sqrt{6}-12\sqrt{6}$$

Combine 27\sqrt{6} and -12\sqrt{6} to get 15\sqrt{6}.

$$15\sqrt{6}$$