Solve sqrt{12}divsqrt{72}

$$\sqrt{ 12 } \div \sqrt{ 72 }$$

Evaluate

$$\frac{\sqrt{6}}{6}\approx 0.40824829$$

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}.

$$\frac{2\sqrt{3}}{\sqrt{72}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{2\sqrt{3}}{6\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

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

Rationalize the denominator of \frac{\sqrt{3}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{6}}{6}$$