Solve sqrt{2^12*3^12/6}

$$\sqrt { \frac { 2 ^ { 12 } \times 3 ^ { 12 } } { 6 } }$$

Evaluate

$$7776\sqrt{6}\approx 19047.232239882$$

Solution Steps

Calculate 2 to the power of 12 and get 4096.

$$\sqrt{\frac{4096\times 3^{12}}{6}}$$

Calculate 3 to the power of 12 and get 531441.

$$\sqrt{\frac{4096\times 531441}{6}}$$

Multiply 4096 and 531441 to get 2176782336.

$$\sqrt{\frac{2176782336}{6}}$$

Divide 2176782336 by 6 to get 362797056.

$$\sqrt{362797056}$$

Factor 362797056=7776^{2}\times 6. Rewrite the square root of the product \sqrt{7776^{2}\times 6} as the product of square roots \sqrt{7776^{2}}\sqrt{6}. Take the square root of 7776^{2}.

$$7776\sqrt{6}$$