Solve frac{sqrt{75}}{sqrt{18}}

$$\frac { \sqrt { 75 } } { \sqrt { 18 } }$$

Evaluate

$$\frac{5\sqrt{6}}{6}\approx 2.041241452$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{5\sqrt{3}}{\sqrt{18}}$$

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}.

$$\frac{5\sqrt{3}}{3\sqrt{2}}$$

Rationalize the denominator of \frac{5\sqrt{3}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{3}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{5\sqrt{3}\sqrt{2}}{3\times 2}$$

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

$$\frac{5\sqrt{6}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{5\sqrt{6}}{6}$$