Solve 2sqrt{54}+3sqrt{96}-4sqrt{216}=

$$2 \sqrt { 54 } + 3 \sqrt { 96 } - 4 \sqrt { 216 } =$$

Evaluate

$$-6\sqrt{6}\approx -14.696938457$$

Solution Steps

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}.

$$2\times 3\sqrt{6}+3\sqrt{96}-4\sqrt{216}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{6}+3\sqrt{96}-4\sqrt{216}$$

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}.

$$6\sqrt{6}+3\times 4\sqrt{6}-4\sqrt{216}$$

Multiply 3 and 4 to get 12.

$$6\sqrt{6}+12\sqrt{6}-4\sqrt{216}$$

Combine 6\sqrt{6} and 12\sqrt{6} to get 18\sqrt{6}.

$$18\sqrt{6}-4\sqrt{216}$$

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$18\sqrt{6}-4\times 6\sqrt{6}$$

Multiply -4 and 6 to get -24.

$$18\sqrt{6}-24\sqrt{6}$$

Combine 18\sqrt{6} and -24\sqrt{6} to get -6\sqrt{6}.

$$-6\sqrt{6}$$