Solve 16/sqrt{41-5}

$$\frac { 16 } { \sqrt { 41 } - 5 }$$

Evaluate

$$\sqrt{41}+5\approx 11.403124237$$

Solution Steps

Rationalize the denominator of \frac{16}{\sqrt{41}-5} by multiplying numerator and denominator by \sqrt{41}+5.

$$\frac{16\left(\sqrt{41}+5\right)}{\left(\sqrt{41}-5\right)\left(\sqrt{41}+5\right)}$$

Consider \left(\sqrt{41}-5\right)\left(\sqrt{41}+5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{16\left(\sqrt{41}+5\right)}{\left(\sqrt{41}\right)^{2}-5^{2}}$$

Square \sqrt{41}. Square 5.

$$\frac{16\left(\sqrt{41}+5\right)}{41-25}$$

Subtract 25 from 41 to get 16.

$$\frac{16\left(\sqrt{41}+5\right)}{16}$$

Cancel out 16 and 16.

$$\sqrt{41}+5$$