Solve frac{sqrt{12}}{sqrt{27}}*sqrt{18}

$$\frac { \sqrt { 12 } } { \sqrt { 27 } } \times \sqrt { 18 }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

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}.

$$\frac{2\sqrt{3}}{3\sqrt{3}}\sqrt{18}$$

Cancel out \sqrt{3} in both numerator and denominator.

$$\frac{2}{3}\sqrt{18}$$

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}.

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

Cancel out 3 and 3.

$$2\sqrt{2}$$