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

$$\frac{25\sqrt{16891}}{889}\approx 3.65481946$$

Solution Steps

Add 2,1 and 3,26 to get 5,36.

$$\frac{380}{\sqrt{\left(\frac{5,36}{0,2}\right)^{2}+3\times 58^{2}}}$$

Expand \frac{5,36}{0,2} by multiplying both numerator and the denominator by 100.

$$\frac{380}{\sqrt{\left(\frac{536}{20}\right)^{2}+3\times 58^{2}}}$$

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

$$\frac{380}{\sqrt{\left(\frac{134}{5}\right)^{2}+3\times 58^{2}}}$$

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

$$\frac{380}{\sqrt{\frac{17956}{25}+3\times 58^{2}}}$$

Calculate 58 to the power of 2 and get 3364.

$$\frac{380}{\sqrt{\frac{17956}{25}+3\times 3364}}$$

Multiply 3 and 3364 to get 10092.

$$\frac{380}{\sqrt{\frac{17956}{25}+10092}}$$

Add \frac{17956}{25} and 10092 to get \frac{270256}{25}.

$$\frac{380}{\sqrt{\frac{270256}{25}}}$$

Rewrite the square root of the division \sqrt{\frac{270256}{25}} as the division of square roots \frac{\sqrt{270256}}{\sqrt{25}}.

$$\frac{380}{\frac{\sqrt{270256}}{\sqrt{25}}}$$

Factor 270256=4^{2}\times 16891. Rewrite the square root of the product \sqrt{4^{2}\times 16891} as the product of square roots \sqrt{4^{2}}\sqrt{16891}. Take the square root of 4^{2}.

$$\frac{380}{\frac{4\sqrt{16891}}{\sqrt{25}}}$$

Calculate the square root of 25 and get 5.

$$\frac{380}{\frac{4\sqrt{16891}}{5}}$$

Divide 380 by \frac{4\sqrt{16891}}{5} by multiplying 380 by the reciprocal of \frac{4\sqrt{16891}}{5}.

$$\frac{380\times 5}{4\sqrt{16891}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{5\times 95}{\sqrt{16891}}$$

Rationalize the denominator of \frac{5\times 95}{\sqrt{16891}} by multiplying numerator and denominator by \sqrt{16891}.

$$\frac{5\times 95\sqrt{16891}}{\left(\sqrt{16891}\right)^{2}}$$

The square of \sqrt{16891} is 16891.

$$\frac{5\times 95\sqrt{16891}}{16891}$$

Multiply 5 and 95 to get 475.

$$\frac{475\sqrt{16891}}{16891}$$

Divide 475\sqrt{16891} by 16891 to get \frac{25}{889}\sqrt{16891}.

$$\frac{25}{889}\sqrt{16891}$$