Solve 6/sqrt{18}

$$\frac { 6 } { \sqrt { 18 } }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

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}.

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

Rationalize the denominator of \frac{6}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{6\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Cancel out 2\times 3 in both numerator and denominator.

$$\sqrt{2}$$