Solve -6/1+sqrt{7}

$$\frac { - 6 } { 1 + \sqrt { 7 } }$$

Evaluate

$$1-\sqrt{7}\approx -1.645751311$$

Solution Steps

Rationalize the denominator of \frac{-6}{1+\sqrt{7}} by multiplying numerator and denominator by 1-\sqrt{7}.

$$\frac{-6\left(1-\sqrt{7}\right)}{\left(1+\sqrt{7}\right)\left(1-\sqrt{7}\right)}$$

Consider \left(1+\sqrt{7}\right)\left(1-\sqrt{7}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-6\left(1-\sqrt{7}\right)}{1^{2}-\left(\sqrt{7}\right)^{2}}$$

Square 1. Square \sqrt{7}.

$$\frac{-6\left(1-\sqrt{7}\right)}{1-7}$$

Subtract 7 from 1 to get -6.

$$\frac{-6\left(1-\sqrt{7}\right)}{-6}$$

Cancel out -6 and -6.

$$1-\sqrt{7}$$