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

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

Evaluate

$$\frac{\sqrt{70}}{35}\approx 0.239045722$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{2}{\sqrt{25+3^{2}+4^{2}+4^{2}+2^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2}{\sqrt{25+9+4^{2}+4^{2}+2^{2}}}$$

Add 25 and 9 to get 34.

$$\frac{2}{\sqrt{34+4^{2}+4^{2}+2^{2}}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{2}{\sqrt{34+16+4^{2}+2^{2}}}$$

Add 34 and 16 to get 50.

$$\frac{2}{\sqrt{50+4^{2}+2^{2}}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{2}{\sqrt{50+16+2^{2}}}$$

Add 50 and 16 to get 66.

$$\frac{2}{\sqrt{66+2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{\sqrt{66+4}}$$

Add 66 and 4 to get 70.

$$\frac{2}{\sqrt{70}}$$

Rationalize the denominator of \frac{2}{\sqrt{70}} by multiplying numerator and denominator by \sqrt{70}.

$$\frac{2\sqrt{70}}{\left(\sqrt{70}\right)^{2}}$$

The square of \sqrt{70} is 70.

$$\frac{2\sqrt{70}}{70}$$

Divide 2\sqrt{70} by 70 to get \frac{1}{35}\sqrt{70}.

$$\frac{1}{35}\sqrt{70}$$