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

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

Evaluate

$$\frac{19000\sqrt{1827641}}{1827641}\approx 14.054265543$$

Solution Steps

Add 2.1 and 3.26 to get 5.36.

$$\frac{380}{\sqrt{\left(\frac{5.36}{0.2}\right)^{2}+3.58^{2}}}$$

Expand \frac{5.36}{0.2} by multiplying both numerator and the denominator by 100.

$$\frac{380}{\sqrt{\left(\frac{536}{20}\right)^{2}+3.58^{2}}}$$

Reduce the fraction \frac{536}{20} to lowest terms by extracting and canceling out 4.

$$\frac{380}{\sqrt{\left(\frac{134}{5}\right)^{2}+3.58^{2}}}$$

Calculate \frac{134}{5} to the power of 2 and get \frac{17956}{25}.

$$\frac{380}{\sqrt{\frac{17956}{25}+3.58^{2}}}$$

Calculate 3.58 to the power of 2 and get 12.8164.

$$\frac{380}{\sqrt{\frac{17956}{25}+12.8164}}$$

Add \frac{17956}{25} and 12.8164 to get \frac{1827641}{2500}.

$$\frac{380}{\sqrt{\frac{1827641}{2500}}}$$

Rewrite the square root of the division \sqrt{\frac{1827641}{2500}} as the division of square roots \frac{\sqrt{1827641}}{\sqrt{2500}}.

$$\frac{380}{\frac{\sqrt{1827641}}{\sqrt{2500}}}$$

Calculate the square root of 2500 and get 50.

$$\frac{380}{\frac{\sqrt{1827641}}{50}}$$

Divide 380 by \frac{\sqrt{1827641}}{50} by multiplying 380 by the reciprocal of \frac{\sqrt{1827641}}{50}.

$$\frac{380\times 50}{\sqrt{1827641}}$$

Rationalize the denominator of \frac{380\times 50}{\sqrt{1827641}} by multiplying numerator and denominator by \sqrt{1827641}.

$$\frac{380\times 50\sqrt{1827641}}{\left(\sqrt{1827641}\right)^{2}}$$

The square of \sqrt{1827641} is 1827641.

$$\frac{380\times 50\sqrt{1827641}}{1827641}$$

Multiply 380 and 50 to get 19000.

$$\frac{19000\sqrt{1827641}}{1827641}$$