Solve frac{sqrt{75}}{sqrt{8}}

$$\frac { \sqrt { 75 } } { \sqrt { 8 } }$$

Evaluate

$$\frac{5\sqrt{6}}{4}\approx 3.061862178$$

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}.

$$\frac{5\sqrt{3}}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 2 and 2 to get 4.

$$\frac{5\sqrt{6}}{4}$$