Rationalizing a Denominator

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Del curso dictado por University of California, Irvine

Pre-Calculus: Functions

315 calificaciones

University of California, Irvine

Pre-Calculus: Functions

315 calificaciones

This course covers mathematical topics in college algebra, with an emphasis on functions. The course is designed to help prepare students to enroll for a first semester course in single variable calculus. Upon completing this course, you will be able to: 1. Solve linear and quadratic equations 2. Solve some classes of rational and radical equations 3. Graph polynomial, rational, piece-wise, exponential and logarithmic functions 4. Find integer roots of polynomial equations 5. Solve exponential and logarithm equations 6. Understand the inverse relations between exponential and logarithm equations 7. Compute values of exponential and logarithm expressions using basic properties

De la lección

Course Overview and Algebra Review

We begin with an overview of the course and an opportunity to review and practice some of the prerequisite algebra skills needed for success in this course.

Properties of Integer Exponents 9:31

Adding and Subtracting Polynomials 8:32

Multiplication of Binomials 10:18

Multiplication of Polynomials 4:14

Multiple Operations with Polynomials 6:42

Rational Exponents 4:29

Simplified Radical Form 7:02

Square Root Addition and Subtraction 6:37

Multiplication Involving Square Roots 5:33

Rationalizing a Denominator 3:48

Conoce a los instructores

Dr. Sarah Eichhorn
Associate Dean, Distance Learning & Tenured Lecturer
Dr. Rachel Cohen Lehman

[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.

[MUSIC]

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