Solve sqrt{3^2+2^4/2^5div2^3}

$$\sqrt { \frac { 3 ^ { 2 } + 2 ^ { 4 } } { 2 ^ { 5 } \div 2 ^ { 3 } } }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

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

Calculate 3 to the power of 2 and get 9.

$$\sqrt{\frac{9+2^{4}}{2^{2}}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt{\frac{9+16}{2^{2}}}$$

Add 9 and 16 to get 25.

$$\sqrt{\frac{25}{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{\frac{25}{4}}$$

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$