Simplifying radical expressions

**jscalalamoboy** · May 20th 2008, 06:16 PM

k... so...

How do you simplify these when they are in fraction form.
1. A radical over a radical
2. A radical over a non radical
3. A non radical over a radical?

All help greatly appriciated!

[JSC]AL(AL)AMOBOY

**Mathstud28** · May 20th 2008, 08:17 PM

Originally Posted by jscalalamoboy

k... so...

How do you simplify these when they are in fraction form.
1. A radical over a radical
2. A radical over a non radical
3. A non radical over a radical?

All help greatly appriciated!

[JSC]AL(AL)AMOBOY

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

$\frac{\sqrt{a}}{b}$ no need for simplification

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

In upper math you (or from what I have seen) rarely do this

**Moo** · May 21st 2008, 12:37 AM

Hello,

Originally Posted by Mathstud28

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

Be careful for this one

If you have $\sqrt{ab}$ , it isn't necessarily equal to $\sqrt{a} \sqrt{b}$ .

Because a and b can be both negative.

$\sqrt{ab}$ will be defined, but not $\sqrt{a}\sqrt{b}$

For example, let's take a=-2 and b=-3.

$\sqrt{ab}=\sqrt{(-2)(-3)}=\sqrt{6}$

But $\sqrt{a} \sqrt{b}=\sqrt{-2} \sqrt{-3}$

Which is... weird

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