# How do you rationalize the denominator and simplify 1/sqrty?

May 31, 2016

$\frac{1}{\sqrt{y}} \equiv \frac{\sqrt{y}}{y}$

The $\equiv$ means 'equivalent to'.

#### Explanation:

Mathematicians do not like a root to be in the denominator if at all possible. Consequently you should always look to remove it if able. Unless instructed otherwise.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply by 1 and you do not change the value. However the value of 1 comes in many forms so you may change the way something looks without changing its intrinsic value.

Given:$\text{ } \frac{1}{\sqrt{y}}$

Multiply by 1 but in the form of $1 = \frac{\sqrt{y}}{\sqrt{y}}$ giving:

$\text{ } \frac{1}{\sqrt{y}} \times \frac{\sqrt{y}}{\sqrt{y}} = \frac{\sqrt{y}}{y}$

Hence the rationalised denominator condition is:$\text{ } \frac{\sqrt{y}}{y}$