Solve 3/sqrt{18}-sqrt{72}:50

$$\frac { 3 } { \sqrt { 18 } } - \sqrt { 72 } : 50$$

Evaluate

$$\frac{19\sqrt{2}}{50}\approx 0.537401154$$

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}.

$$\frac{3}{3\sqrt{2}}-\frac{\sqrt{72}}{50}$$

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

$$\frac{3\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}-\frac{\sqrt{72}}{50}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{3\times 2}-\frac{\sqrt{72}}{50}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{72}}{50}$$

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}.

$$\frac{\sqrt{2}}{2}-\frac{6\sqrt{2}}{50}$$

Divide 6\sqrt{2} by 50 to get \frac{3}{25}\sqrt{2}.

$$\frac{\sqrt{2}}{2}-\frac{3}{25}\sqrt{2}$$

Combine \frac{\sqrt{2}}{2} and -\frac{3}{25}\sqrt{2} to get \frac{19}{50}\sqrt{2}.

$$\frac{19}{50}\sqrt{2}$$