Solve frac{6sqrt{27}}{sqrt{12}}

$$\frac { 6 \sqrt { 27 } } { \sqrt { 12 } }$$

Evaluate

$$9$$

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}.

$$\frac{6\times 3\sqrt{3}}{\sqrt{12}}$$

Multiply 6 and 3 to get 18.

$$\frac{18\sqrt{3}}{\sqrt{12}}$$

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}.

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

Cancel out 2\sqrt{3} in both numerator and denominator.

$$9$$

Factor

$$3^{2}$$