Solve 7/sqrt{3-sqrt{2}}

$$\frac{ 7 }{ \sqrt{ 3 } - \sqrt{ 2 } }$$

Evaluate

$$7\left(\sqrt{2}+\sqrt{3}\right)\approx 22.02385059$$

Solution Steps

Rationalize the denominator of \frac{7}{\sqrt{3}-\sqrt{2}} by multiplying numerator and denominator by \sqrt{3}+\sqrt{2}.

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

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

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

Square \sqrt{3}. Square \sqrt{2}.

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

Subtract 2 from 3 to get 1.

$$\frac{7\left(\sqrt{3}+\sqrt{2}\right)}{1}$$

Anything divided by one gives itself.

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

Use the distributive property to multiply 7 by \sqrt{3}+\sqrt{2}.

$$7\sqrt{3}+7\sqrt{2}$$