Exercises: Terms with Square Roots

We would like to show that $\frac{1}{\sqrt{a}}=\frac{\sqrt{a}}{a}$

Try to make the denominator rational for this.

$\frac{1}{\sqrt{a}}$

Expand by $\sqrt{a}$

$=\frac{1\cdot \sqrt{a}}{\sqrt{a}\cdot \sqrt{a}}$

Use the calculation rules for the product of roots.

$=\frac{1\cdot \sqrt{a}}{\sqrt{a\cdot a}}$

The square and the root cancel each other.

$=\frac{\sqrt{a}}{a}$