Solve 16/sqrt{12^{2+8^2+16^2+8^2+16^2}}=

$$\frac { 16 } { \sqrt { 12 ^ { 2 } + 8 ^ { 2 } + 16 ^ { 2 } + 8 ^ { 2 } + 16 ^ { 2 } } } =$$

Evaluate

$$\frac{4}{7}\approx 0.571428571$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\frac{16}{\sqrt{144+8^{2}+16^{2}+8^{2}+16^{2}}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{16}{\sqrt{144+64+16^{2}+8^{2}+16^{2}}}$$

Add 144 and 64 to get 208.

$$\frac{16}{\sqrt{208+16^{2}+8^{2}+16^{2}}}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{16}{\sqrt{208+256+8^{2}+16^{2}}}$$

Add 208 and 256 to get 464.

$$\frac{16}{\sqrt{464+8^{2}+16^{2}}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{16}{\sqrt{464+64+16^{2}}}$$

Add 464 and 64 to get 528.

$$\frac{16}{\sqrt{528+16^{2}}}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{16}{\sqrt{528+256}}$$

Add 528 and 256 to get 784.

$$\frac{16}{\sqrt{784}}$$

Calculate the square root of 784 and get 28.

$$\frac{16}{28}$$

Reduce the fraction \frac{16}{28} to lowest terms by extracting and canceling out 4.

$$\frac{4}{7}$$

Factor

$$\frac{2 ^ {2}}{7} = 0.5714285714285714$$