Solve 4/sqrt{2-7}

$$\frac { 4 } { \sqrt { 2 } - 7 }$$

Evaluate

$$\frac{-4\sqrt{2}-28}{47}\approx -0.716103282$$

Solution Steps

Rationalize the denominator of \frac{4}{\sqrt{2}-7} by multiplying numerator and denominator by \sqrt{2}+7.

$$\frac{4\left(\sqrt{2}+7\right)}{\left(\sqrt{2}-7\right)\left(\sqrt{2}+7\right)}$$

Consider \left(\sqrt{2}-7\right)\left(\sqrt{2}+7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{4\left(\sqrt{2}+7\right)}{\left(\sqrt{2}\right)^{2}-7^{2}}$$

Square \sqrt{2}. Square 7.

$$\frac{4\left(\sqrt{2}+7\right)}{2-49}$$

Subtract 49 from 2 to get -47.

$$\frac{4\left(\sqrt{2}+7\right)}{-47}$$

Use the distributive property to multiply 4 by \sqrt{2}+7.

$$\frac{4\sqrt{2}+28}{-47}$$