Solve 3sqrt{27}div(3sqrt{1/18})-2sqrt{3}

$$3 \sqrt { 27 } \div ( 3 \sqrt { \frac { 1 } { 18 } } ) - 2 \sqrt { 3 }$$

Evaluate

$$9\sqrt{6}-2\sqrt{3}\approx 18.58130607$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{27}}{\sqrt{\frac{1}{18}}}-2\sqrt{3}$$

Rewrite the division of square roots \frac{\sqrt{27}}{\sqrt{\frac{1}{18}}} as the square root of the division \sqrt{\frac{27}{\frac{1}{18}}} and perform the division.

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

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}.

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

Combine 3\sqrt{3} and -2\sqrt{3} to get \sqrt{3}.

$$\sqrt{3}$$

Factor

$$9 \sqrt{6} - 2 \sqrt{3} = 18.58130607$$