Solve frac{sqrt{27}}{3}-3sqrt{18}

$$\frac { \sqrt { 27 } } { 3 } - 3 \sqrt { 18 }$$

Evaluate

$$\sqrt{3}-9\sqrt{2}\approx -10.995871254$$

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}.

$$\frac{3\sqrt{3}}{3}-3\sqrt{18}$$

Cancel out 3 and 3.

$$\sqrt{3}-3\sqrt{18}$$

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}.

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

Multiply -3 and 3 to get -9.

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

Factor

$$\sqrt{3} - 9 \sqrt{2} = -10.995871254$$