Solve frac{sqrt{4^2*2+8*2^2}}{4^2}

$$\frac { \sqrt { 4 ^ { 2 } \cdot 2 + 8 \cdot 2 ^ { 2 } } } { 4 ^ { 2 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{\sqrt{16\times 2+8\times 2^{2}}}{4^{2}}$$

Multiply 16 and 2 to get 32.

$$\frac{\sqrt{32+8\times 2^{2}}}{4^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\sqrt{32+8\times 4}}{4^{2}}$$

Multiply 8 and 4 to get 32.

$$\frac{\sqrt{32+32}}{4^{2}}$$

Add 32 and 32 to get 64.

$$\frac{\sqrt{64}}{4^{2}}$$

Calculate the square root of 64 and get 8.

$$\frac{8}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{8}{16}$$

Reduce the fraction \frac{8}{16} to lowest terms by extracting and canceling out 8.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$