Solve sqrt{4!}*sqrt{3!}=?

$$\sqrt { 4 ! } \cdot \sqrt { 3 ! } = ?$$

Evaluate

$$12$$

Solution Steps

The factorial of 4 is 24.

$$\sqrt{24}\sqrt{3!}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$2\sqrt{6}\sqrt{3!}$$

The factorial of 3 is 6.

$$2\sqrt{6}\sqrt{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$2\times 6$$

Multiply 2 and 6 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$