Solve 6/sqrt{7+2}

$$\frac { 6 } { \sqrt { 7 } + 2 }$$

Evaluate

$$2\left(\sqrt{7}-2\right)\approx 1.291502622$$

Solution Steps

Rationalize the denominator of \frac{6}{\sqrt{7}+2} by multiplying numerator and denominator by \sqrt{7}-2.

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

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}.

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

Square \sqrt{7}. Square 2.

$$\frac{6\left(\sqrt{7}-2\right)}{7-4}$$

Subtract 4 from 7 to get 3.

$$\frac{6\left(\sqrt{7}-2\right)}{3}$$

Divide 6\left(\sqrt{7}-2\right) by 3 to get 2\left(\sqrt{7}-2\right).

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

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

$$2\sqrt{7}-4$$