Solve frac{{left(sqrt{20}right)}^2-{left(sqrt{13}right)}^2-5^2}{2sqrt{13}*5}

$$\frac{ { \left( \sqrt{ 20 } \right) }^{ 2 } - { \left( \sqrt{ 13 } \right) }^{ 2 } - { 5 }^{ 2 } }{ 2 \sqrt{ 13 } \times 5 }$$

Evaluate

$$-\frac{9\sqrt{13}}{65}\approx -0.499230177$$

Solution Steps

The square of \sqrt{20} is 20.

$$\frac{20-\left(\sqrt{13}\right)^{2}-5^{2}}{2\times 5\sqrt{13}}$$

The square of \sqrt{13} is 13.

$$\frac{20-13-5^{2}}{2\times 5\sqrt{13}}$$

Subtract 13 from 20 to get 7.

$$\frac{7-5^{2}}{2\times 5\sqrt{13}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{7-25}{2\times 5\sqrt{13}}$$

Subtract 25 from 7 to get -18.

$$\frac{-18}{2\times 5\sqrt{13}}$$

Multiply 2 and 5 to get 10.

$$\frac{-18}{10\sqrt{13}}$$

Rationalize the denominator of \frac{-18}{10\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{-18\sqrt{13}}{10\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{-18\sqrt{13}}{10\times 13}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-9\sqrt{13}}{5\times 13}$$

Multiply 5 and 13 to get 65.

$$\frac{-9\sqrt{13}}{65}$$