1. Dividing Radicals

2. Dividing Radicals – the Basics
Like with multiplying radicals, to divide radicals they must have the same INDEX.
Remember, division is often written as a fraction.
As with multiplying radicals, you can divide/reduce the coefficients to get the coefficient of the quotient, then divide/reduce the radicand to get the radicand of the quotient.
The final basic fact you need to know is: to take the root of a fraction, you take the root of both the numerator and denominator.
Lets try some examples…

3. Are the indices the same? YEP!!! Let’s do this!
Divide num. & denom. by 2
Divide num. & denom. by 3
Divide num. & denom. by 25
Are the indices the same?
YEP!!! Let’s do this!
Divide/reduce the coefficients and radicands.
Simplify your radical
Are the indices the same?
YEP!!! Let’s do this!
Divide/reduce the coefficients and radicands.
Simplify your radical.
What happened to the denominator?
Final check: are your radical and fraction completely simplified?

4. How do I take the square root of a fraction?
Take the square root of the numerator and denominator separately. But make your life easier – simplify your fraction first.
Now split it up and simplify.
Divide num. & denom. by 7

5. One of those really important math rules….
You know you need to simplify fractions completely, combine like terms, simplify radicand, etc. before you can say you have ‘finished’ a problem.
One other rule you need to know is that you NEVER leave a radical in the denominator of a fraction!
We will use our knowledge of simplifying radicals and of equivalent fractions to make sure we don’t break this rule!

6. Rationalizing Denominators
Final check: are your radical and fraction completely simplified?
Step 1 – simplify our fraction
Step 2 – simplify our radicands
Step 3 – rationalize the denominator
Why do we still have a radical in the denominator? What would we need for the radical to simplify?