Solve 2/1-sqrt{10}

$$\frac { 2 } { 1 - \sqrt { 10 } }$$

Evaluate

$$\frac{-2\sqrt{10}-2}{9}\approx -0.924950591$$

Solution Steps

Rationalize the denominator of \frac{2}{1-\sqrt{10}} by multiplying numerator and denominator by 1+\sqrt{10}.

$$\frac{2\left(1+\sqrt{10}\right)}{\left(1-\sqrt{10}\right)\left(1+\sqrt{10}\right)}$$

Consider \left(1-\sqrt{10}\right)\left(1+\sqrt{10}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(1+\sqrt{10}\right)}{1^{2}-\left(\sqrt{10}\right)^{2}}$$

Square 1. Square \sqrt{10}.

$$\frac{2\left(1+\sqrt{10}\right)}{1-10}$$

Subtract 10 from 1 to get -9.

$$\frac{2\left(1+\sqrt{10}\right)}{-9}$$

Use the distributive property to multiply 2 by 1+\sqrt{10}.

$$\frac{2+2\sqrt{10}}{-9}$$