Solve 14/3-sqrt{2}

$$\frac{ 14 }{ 3- \sqrt{ 2 } }$$

Evaluate

$$2\sqrt{2}+6\approx 8.828427125$$

Solution Steps

Rationalize the denominator of \frac{14}{3-\sqrt{2}} by multiplying numerator and denominator by 3+\sqrt{2}.

$$\frac{14\left(3+\sqrt{2}\right)}{\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)}$$

Consider \left(3-\sqrt{2}\right)\left(3+\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}.

$$\frac{14\left(3+\sqrt{2}\right)}{3^{2}-\left(\sqrt{2}\right)^{2}}$$

Square 3. Square \sqrt{2}.

$$\frac{14\left(3+\sqrt{2}\right)}{9-2}$$

Subtract 2 from 9 to get 7.

$$\frac{14\left(3+\sqrt{2}\right)}{7}$$

Divide 14\left(3+\sqrt{2}\right) by 7 to get 2\left(3+\sqrt{2}\right).

$$2\left(3+\sqrt{2}\right)$$

Use the distributive property to multiply 2 by 3+\sqrt{2}.

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