Solve 7/6-sqrt{2}

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

Evaluate

$$\frac{7\left(\sqrt{2}+6\right)}{34}\approx 1.526455733$$

Solution Steps

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

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

Consider \left(6-\sqrt{2}\right)\left(6+\sqrt{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}.

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

Square 6. Square \sqrt{2}.

$$\frac{7\left(6+\sqrt{2}\right)}{36-2}$$

Subtract 2 from 36 to get 34.

$$\frac{7\left(6+\sqrt{2}\right)}{34}$$

Use the distributive property to multiply 7 by 6+\sqrt{2}.

$$\frac{42+7\sqrt{2}}{34}$$