Solve sqrt{(15+6)^2/5!}

$$\sqrt { \frac { ( 15 + 6 ) ^ { 2 } } { 5 ! } }$$

Evaluate

$$\frac{7\sqrt{30}}{20}\approx 1.917028951$$

Solution Steps

Add 15 and 6 to get 21.

$$\sqrt{\frac{21^{2}}{5!}}$$

Calculate 21 to the power of 2 and get 441.

$$\sqrt{\frac{441}{5!}}$$

The factorial of 5 is 120.

$$\sqrt{\frac{441}{120}}$$

Reduce the fraction \frac{441}{120} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{147}{40}}$$

Rewrite the square root of the division \sqrt{\frac{147}{40}} as the division of square roots \frac{\sqrt{147}}{\sqrt{40}}.

$$\frac{\sqrt{147}}{\sqrt{40}}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$\frac{7\sqrt{3}}{\sqrt{40}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{7\sqrt{3}}{2\sqrt{10}}$$

Rationalize the denominator of \frac{7\sqrt{3}}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{7\sqrt{3}\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{7\sqrt{3}\sqrt{10}}{2\times 10}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{7\sqrt{30}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{7\sqrt{30}}{20}$$