Solve 8+13-25/2*2sqrt{2sqrt{13}}

$$\frac{ 8+13-25 }{ 2 \cdot 2 \sqrt{ 2 } \sqrt{ 13 } }$$

Evaluate

$$-\frac{\sqrt{26}}{26}\approx -0.196116135$$

Solution Steps

Add 8 and 13 to get 21.

$$\frac{21-25}{2\times 2\sqrt{2}\sqrt{13}}$$

Subtract 25 from 21 to get -4.

$$\frac{-4}{2\times 2\sqrt{2}\sqrt{13}}$$

Multiply 2 and 2 to get 4.

$$\frac{-4}{4\sqrt{2}\sqrt{13}}$$

To multiply \sqrt{2} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{-4}{4\sqrt{26}}$$

Rationalize the denominator of \frac{-4}{4\sqrt{26}} by multiplying numerator and denominator by \sqrt{26}.

$$\frac{-4\sqrt{26}}{4\left(\sqrt{26}\right)^{2}}$$

The square of \sqrt{26} is 26.

$$\frac{-4\sqrt{26}}{4\times 26}$$

Cancel out 4 in both numerator and denominator.

$$\frac{-\sqrt{26}}{26}$$