Solve 380/sqrt{frac{(2.1+3.26)^2{0.2}+3.58^2}}

$$\frac { 380 } { \sqrt { \frac { ( 2.1 + 3.26 ) ^ { 2 } } { 0.2 } + 3.58 ^ { 2 } } }$$

Evaluate

$$\frac{19000\sqrt{391161}}{391161}\approx 30.379164608$$

Solution Steps

Add 2.1 and 3.26 to get 5.36.

$$\frac{380}{\sqrt{\frac{5.36^{2}}{0.2}+3.58^{2}}}$$

Calculate 5.36 to the power of 2 and get 28.7296.

$$\frac{380}{\sqrt{\frac{28.7296}{0.2}+3.58^{2}}}$$

Expand \frac{28.7296}{0.2} by multiplying both numerator and the denominator by 10000.

$$\frac{380}{\sqrt{\frac{287296}{2000}+3.58^{2}}}$$

Reduce the fraction \frac{287296}{2000} to lowest terms by extracting and canceling out 16.

$$\frac{380}{\sqrt{\frac{17956}{125}+3.58^{2}}}$$

Calculate 3.58 to the power of 2 and get 12.8164.

$$\frac{380}{\sqrt{\frac{17956}{125}+12.8164}}$$

Add \frac{17956}{125} and 12.8164 to get \frac{391161}{2500}.

$$\frac{380}{\sqrt{\frac{391161}{2500}}}$$

Rewrite the square root of the division \sqrt{\frac{391161}{2500}} as the division of square roots \frac{\sqrt{391161}}{\sqrt{2500}}.

$$\frac{380}{\frac{\sqrt{391161}}{\sqrt{2500}}}$$

Calculate the square root of 2500 and get 50.

$$\frac{380}{\frac{\sqrt{391161}}{50}}$$

Divide 380 by \frac{\sqrt{391161}}{50} by multiplying 380 by the reciprocal of \frac{\sqrt{391161}}{50}.

$$\frac{380\times 50}{\sqrt{391161}}$$

Rationalize the denominator of \frac{380\times 50}{\sqrt{391161}} by multiplying numerator and denominator by \sqrt{391161}.

$$\frac{380\times 50\sqrt{391161}}{\left(\sqrt{391161}\right)^{2}}$$

The square of \sqrt{391161} is 391161.

$$\frac{380\times 50\sqrt{391161}}{391161}$$

Multiply 380 and 50 to get 19000.

$$\frac{19000\sqrt{391161}}{391161}$$