Solve sqrt{2}divsqrt{18}

$$\sqrt{ 2 } \div \sqrt{ 18 }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

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}.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 3 and 2 to get 6.

$$\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Factor

$$\frac{1}{3} = 0.3333333333333333$$