Solve sqrt{2^2+5^0+11/5^2-2*2^3}=

$$\sqrt { \frac { 2 ^ { 2 } + 5 ^ { 0 } + 11 } { 5 ^ { 2 } - 2 \cdot 2 ^ { 3 } } } =$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\sqrt{\frac{2^{2}+5^{0}+11}{5^{2}-2^{4}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{\frac{4+5^{0}+11}{5^{2}-2^{4}}}$$

Calculate 5 to the power of 0 and get 1.

$$\sqrt{\frac{4+1+11}{5^{2}-2^{4}}}$$

Add 4 and 1 to get 5.

$$\sqrt{\frac{5+11}{5^{2}-2^{4}}}$$

Add 5 and 11 to get 16.

$$\sqrt{\frac{16}{5^{2}-2^{4}}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{\frac{16}{25-2^{4}}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt{\frac{16}{25-16}}$$

Subtract 16 from 25 to get 9.

$$\sqrt{\frac{16}{9}}$$

Rewrite the square root of the division \frac{16}{9} as the division of square roots \frac{\sqrt{16}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$