[MUSIC] Let's learn how to Rationalize a Denominator.

For example, let's rationalize the denominator of this expression and write

our answer in simplified form. Looking at this denominator here, we have

an irrational number here and an irrational number here.

Remember to rationalize the denominator, means to make the denominator a rational

number. And we can do that by mulipling Both the

numerator, and denominator, by the conjugate, of the denominator.

And remember the conjugate, is the same expression, but we just change the minus,

to a plus. And if we multiply our denominator by

this we need to multiply our denominator by this as well.

Lets put parentheses here so that we know that we're going to foil both the

numerator and denominator. So what do we get? Looking at the

numerator here we have 3 square root of 2 times 3 square root of 5,

and the square root of 2 times square root of 5 is square root of 10. And 3 *

3=9, so this is equal to 9 square root of 10.

The outer term is 12, square root of 4. The inner term, is -6 square root 25.

And the last term is -8 square root of 10.

What about the denominator? When we foil this out, we have 9 square root of 25,

the outer term is + 12 square root of 10. And the inner term is -12, square root of

10. And the last term is -16, square root of

4. Now by multiplying by the conjugate,

these outer and inner terms in the denominator will cancel.

And what are we left with. We have 9 square root of 10 and then plus

12 square root of 4. But the square root of 4 is 2 so we have

plus 24. And then minus 6 square root of 25 and

square root of 25 is 5. So this is -30 and then -8 square root of

10, divided by we have 9 times the square root of 25, or 9 times 5, which is 45.

And then - 16 times square root of 4, but square root of 4 is 2, so it is -32.

Now let's combine like terms. This 9 square root of 10 - 8 square root

of 10, gives us positive 1 square root 10.

So this is equal to square root of 10. And then 24 - 30 is -6, and the

denominator is 13. And we have rationalized our denominator

and written our answer in simplified form.

So this would be our answer. And this is how we rationalize a

denominator, we multiply both the numerator and denominator by the

conjugate of the denominator. Thank you, and we'll see you next time.