Solve 35-8/sqrt{7-2}

$$\frac { 35 - 8 } { \sqrt { 7 } - 2 }$$

Evaluate

$$9\left(\sqrt{7}+2\right)\approx 41.8117618$$

Solution Steps

Subtract 8 from 35 to get 27.

$$\frac{27}{\sqrt{7}-2}$$

Rationalize the denominator of \frac{27}{\sqrt{7}-2} by multiplying numerator and denominator by \sqrt{7}+2.

$$\frac{27\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}$$

Consider \left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{27\left(\sqrt{7}+2\right)}{\left(\sqrt{7}\right)^{2}-2^{2}}$$

Square \sqrt{7}. Square 2.

$$\frac{27\left(\sqrt{7}+2\right)}{7-4}$$

Subtract 4 from 7 to get 3.

$$\frac{27\left(\sqrt{7}+2\right)}{3}$$

Divide 27\left(\sqrt{7}+2\right) by 3 to get 9\left(\sqrt{7}+2\right).

$$9\left(\sqrt{7}+2\right)$$

Use the distributive property to multiply 9 by \sqrt{7}+2.

$$9\sqrt{7}+18$$