Solve -2sqrt{18}-3sqrt{27}+3sqrt{27}

$$- 2 \sqrt { 18 } - 3 \sqrt { 27 } + 3 \sqrt { 27 }$$

Evaluate

$$-6\sqrt{2}\approx -8.485281374$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$-2\times 3\sqrt{2}-3\sqrt{27}+3\sqrt{27}$$

Multiply -2 and 3 to get -6.

$$-6\sqrt{2}-3\sqrt{27}+3\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$-6\sqrt{2}-3\times 3\sqrt{3}+3\sqrt{27}$$

Multiply -3 and 3 to get -9.

$$-6\sqrt{2}-9\sqrt{3}+3\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Multiply 3 and 3 to get 9.

$$-6\sqrt{2}-9\sqrt{3}+9\sqrt{3}$$

Combine -9\sqrt{3} and 9\sqrt{3} to get 0.

$$-6\sqrt{2}$$