Solve 5sqrt{6}-9sqrt{24}+2sqrt{54}=

$$5 \sqrt { 6 } - 9 \sqrt { 24 } + 2 \sqrt { 54 } =$$

Evaluate

$$-7\sqrt{6}\approx -17.146428199$$

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}.

$$5\sqrt{6}-9\times 2\sqrt{6}+2\sqrt{54}$$

Multiply -9 and 2 to get -18.

$$5\sqrt{6}-18\sqrt{6}+2\sqrt{54}$$

Combine 5\sqrt{6} and -18\sqrt{6} to get -13\sqrt{6}.

$$-13\sqrt{6}+2\sqrt{54}$$

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}.

$$-13\sqrt{6}+2\times 3\sqrt{6}$$

Multiply 2 and 3 to get 6.

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

Combine -13\sqrt{6} and 6\sqrt{6} to get -7\sqrt{6}.

$$-7\sqrt{6}$$