Solve 2/4+sqrt{35}

$$\frac { 2 } { 4 + \sqrt { 35 } }$$

Evaluate

$$\frac{2\left(\sqrt{35}-4\right)}{19}\approx 0.201692609$$

Solution Steps

Rationalize the denominator of \frac{2}{4+\sqrt{35}} by multiplying numerator and denominator by 4-\sqrt{35}.

$$\frac{2\left(4-\sqrt{35}\right)}{\left(4+\sqrt{35}\right)\left(4-\sqrt{35}\right)}$$

Consider \left(4+\sqrt{35}\right)\left(4-\sqrt{35}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(4-\sqrt{35}\right)}{4^{2}-\left(\sqrt{35}\right)^{2}}$$

Square 4. Square \sqrt{35}.

$$\frac{2\left(4-\sqrt{35}\right)}{16-35}$$

Subtract 35 from 16 to get -19.

$$\frac{2\left(4-\sqrt{35}\right)}{-19}$$

Use the distributive property to multiply 2 by 4-\sqrt{35}.

$$\frac{8-2\sqrt{35}}{-19}$$