Solve 1/4sqrt{12}divsqrt{27}

$$\frac { 1 } { 4 } \sqrt { 12 } \div \sqrt { 27 }$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

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}.

$$\frac{\frac{1}{4}\times 2\sqrt{3}}{\sqrt{27}}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{\frac{2}{4}\sqrt{3}}{\sqrt{27}}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

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}.

$$\frac{\frac{1}{2}\sqrt{3}}{3\sqrt{3}}$$

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

$$\frac{\frac{1}{2}}{3}$$

Express \frac{\frac{1}{2}}{3} as a single fraction.

$$\frac{1}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$