Solve frac{sqrt{9}}{pi2}divfrac{sqrt{5}4}{sqrt{12}}

$$\frac { \sqrt { 9 } } { \pi 2 } \div \frac { \sqrt { 5 } 4 } { \sqrt { 12 } }$$

Evaluate

$$\frac{3\sqrt{15}}{20\pi }\approx 0.184921333$$

Short Solution Steps

Divide \frac{\sqrt{9}}{\pi \times 2} by \frac{4\sqrt{5}}{\sqrt{12}} by multiplying \frac{\sqrt{9}}{\pi \times 2} by the reciprocal of \frac{4\sqrt{5}}{\sqrt{12}}.

$$\frac{\sqrt{9}\sqrt{12}}{\pi \times 2\times 4\sqrt{5}}$$

Calculate the square root of 9 and get 3.

$$\frac{3\sqrt{12}}{\pi \times 2\times 4\sqrt{5}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{3\times 2\sqrt{3}}{\pi \times 2\times 4\sqrt{5}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{3}}{\pi \times 2\times 4\sqrt{5}}$$

Multiply 2 and 4 to get 8.

$$\frac{6\sqrt{3}}{\pi \times 8\sqrt{5}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{3}}{4\pi \sqrt{5}}$$

Rationalize the denominator of \frac{3\sqrt{3}}{4\pi \sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{3}\sqrt{5}}{4\pi \left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{3}\sqrt{5}}{4\pi \times 5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{3\sqrt{15}}{4\pi \times 5}$$

Multiply 4 and 5 to get 20.

$$\frac{3\sqrt{15}}{20\pi }$$