Solve 1/sqrt{6-3}

$$\frac { 1 } { \sqrt { 6 } - 3 }$$

Evaluate

$$-\frac{\sqrt{6}}{3}-1\approx -1.816496581$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{6}-3} by multiplying numerator and denominator by \sqrt{6}+3.

$$\frac{\sqrt{6}+3}{\left(\sqrt{6}-3\right)\left(\sqrt{6}+3\right)}$$

Consider \left(\sqrt{6}-3\right)\left(\sqrt{6}+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\sqrt{6}+3}{\left(\sqrt{6}\right)^{2}-3^{2}}$$

Square \sqrt{6}. Square 3.

$$\frac{\sqrt{6}+3}{6-9}$$

Subtract 9 from 6 to get -3.

$$\frac{\sqrt{6}+3}{-3}$$

Multiply both numerator and denominator by -1.

$$\frac{-\sqrt{6}-3}{3}$$