Solve sqrt{2^4*3^8/3^4*2^8}

$$\sqrt { \frac { 2 ^ { 4 } \times 3 ^ { 8 } } { 3 ^ { 4 } \times 2 ^ { 8 } } }$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Cancel out 2^{4}\times 3^{4} in both numerator and denominator.

$$\sqrt{\frac{3^{4}}{2^{4}}}$$

Calculate 3 to the power of 4 and get 81.

$$\sqrt{\frac{81}{2^{4}}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt{\frac{81}{16}}$$

Rewrite the square root of the division \frac{81}{16} as the division of square roots \frac{\sqrt{81}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$