Solve 1715/1-sqrt{5}=

$$\frac { 1715 } { 1 - \sqrt { 5 } } =$$

Evaluate

$$\frac{-1715\sqrt{5}-1715}{4}\approx -1387.464145353$$

Solution Steps

Rationalize the denominator of \frac{1715}{1-\sqrt{5}} by multiplying numerator and denominator by 1+\sqrt{5}.

$$\frac{1715\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)}$$

Consider \left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{1715\left(1+\sqrt{5}\right)}{1^{2}-\left(\sqrt{5}\right)^{2}}$$

Square 1. Square \sqrt{5}.

$$\frac{1715\left(1+\sqrt{5}\right)}{1-5}$$

Subtract 5 from 1 to get -4.

$$\frac{1715\left(1+\sqrt{5}\right)}{-4}$$

Use the distributive property to multiply 1715 by 1+\sqrt{5}.

$$\frac{1715+1715\sqrt{5}}{-4}$$