Solve 3-1/sqrt{3+sqrt{2}}

$$\frac { 3 - 1 } { \sqrt { 3 } + \sqrt { 2 } }$$

Evaluate

$$2\left(\sqrt{3}-\sqrt{2}\right)\approx 0.63567449$$

Solution Steps

Subtract 1 from 3 to get 2.

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

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

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

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}.

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

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

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

Subtract 2 from 3 to get 1.

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

Anything divided by one gives itself.

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

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

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