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

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

Evaluate

$$8\sqrt{2}-9\sqrt{3}\approx -4.274748769$$

Solution Steps

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}.

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

Multiply -3 and 3 to get -9.

$$-9\sqrt{3}-\sqrt{2}+3\sqrt{18}$$

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}.

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

Multiply 3 and 3 to get 9.

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

Combine -\sqrt{2} and 9\sqrt{2} to get 8\sqrt{2}.

$$-9\sqrt{3}+8\sqrt{2}$$