Solve sqrt{3!/6!}*100

$$\sqrt { \frac { 3 ! } { 6 ! } } \times 100$$

Evaluate

$$\frac{5\sqrt{30}}{3}\approx 9.128709292$$

Solution Steps

The factorial of 3 is 6.

$$100\sqrt{\frac{6}{6!}}$$

The factorial of 6 is 720.

$$100\sqrt{\frac{6}{720}}$$

Reduce the fraction \frac{6}{720} to lowest terms by extracting and canceling out 6.

$$100\sqrt{\frac{1}{120}}$$

Rewrite the square root of the division \sqrt{\frac{1}{120}} as the division of square roots \frac{\sqrt{1}}{\sqrt{120}}.

$$100\times \frac{\sqrt{1}}{\sqrt{120}}$$

Calculate the square root of 1 and get 1.

$$100\times \frac{1}{\sqrt{120}}$$

Factor 120=2^{2}\times 30. Rewrite the square root of the product \sqrt{2^{2}\times 30} as the product of square roots \sqrt{2^{2}}\sqrt{30}. Take the square root of 2^{2}.

$$100\times \frac{1}{2\sqrt{30}}$$

Rationalize the denominator of \frac{1}{2\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$100\times \frac{\sqrt{30}}{2\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$100\times \frac{\sqrt{30}}{2\times 30}$$

Multiply 2 and 30 to get 60.

$$100\times \frac{\sqrt{30}}{60}$$

Express 100\times \frac{\sqrt{30}}{60} as a single fraction.

$$\frac{100\sqrt{30}}{60}$$

Divide 100\sqrt{30} by 60 to get \frac{5}{3}\sqrt{30}.

$$\frac{5}{3}\sqrt{30}$$