Solve frac{sqrt{45}}{5sqrt{2}}

$$\frac { \sqrt { 45 } } { 5 \sqrt { 2 } }$$

Evaluate

$$\frac{3\sqrt{10}}{10}\approx 0.948683298$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

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

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

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

The square of \sqrt{2} is 2.

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

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{3\sqrt{10}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{3\sqrt{10}}{10}$$