Solve 3.5-8/sqrt{7-2}

$$\frac { 3.5 - 8 } { \sqrt { 7 } - 2 }$$

Evaluate

$$-\frac{3\sqrt{7}}{2}-3\approx -6.968626967$$

Solution Steps

Subtract 8 from 3.5 to get -4.5.

$$\frac{-4.5}{\sqrt{7}-2}$$

Rationalize the denominator of \frac{-4.5}{\sqrt{7}-2} by multiplying numerator and denominator by \sqrt{7}+2.

$$\frac{-4.5\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}$$

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}.

$$\frac{-4.5\left(\sqrt{7}+2\right)}{\left(\sqrt{7}\right)^{2}-2^{2}}$$

Square \sqrt{7}. Square 2.

$$\frac{-4.5\left(\sqrt{7}+2\right)}{7-4}$$

Subtract 4 from 7 to get 3.

$$\frac{-4.5\left(\sqrt{7}+2\right)}{3}$$

Divide -4.5\left(\sqrt{7}+2\right) by 3 to get -1.5\left(\sqrt{7}+2\right).

$$-1.5\left(\sqrt{7}+2\right)$$

Use the distributive property to multiply -1.5 by \sqrt{7}+2.

$$-1.5\sqrt{7}-3$$