Solve 119-109/frac{13{sqrt{20}}}

$$\frac { 119 - 109 } { \frac { 13 } { \sqrt { 20 } } }$$

Evaluate

$$\frac{20\sqrt{5}}{13}\approx 3.440104581$$

Solution Steps

Subtract 109 from 119 to get 10.

$$\frac{10}{\frac{13}{\sqrt{20}}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{10}{\frac{13}{2\sqrt{5}}}$$

Rationalize the denominator of \frac{13}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{10}{\frac{13\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{10}{\frac{13\sqrt{5}}{2\times 5}}$$

Multiply 2 and 5 to get 10.

$$\frac{10}{\frac{13\sqrt{5}}{10}}$$

Divide 10 by \frac{13\sqrt{5}}{10} by multiplying 10 by the reciprocal of \frac{13\sqrt{5}}{10}.

$$\frac{10\times 10}{13\sqrt{5}}$$

Rationalize the denominator of \frac{10\times 10}{13\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{10\times 10\sqrt{5}}{13\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{10\times 10\sqrt{5}}{13\times 5}$$

Multiply 10 and 10 to get 100.

$$\frac{100\sqrt{5}}{13\times 5}$$

Multiply 13 and 5 to get 65.

$$\frac{100\sqrt{5}}{65}$$

Divide 100\sqrt{5} by 65 to get \frac{20}{13}\sqrt{5}.

$$\frac{20}{13}\sqrt{5}$$