Copyright

Simplify Square Roots of Quotients Video

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Rationalizing Denominators in Radical Expressions

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:02 The Quotient Rule
  • 0:19 Solving with Quotient Rule
  • 1:24 Rationalize the Denominator
  • 4:08 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Jennifer Beddoe
The quotient rule can be used to simplify square roots of quotients. This lesson will define the quotient rule and show you how it is used to simplify square roots.

The Quotient Rule

The quotient rule for radicals says that the radical of a quotient is the quotient of the radicals, which means:


null


Solve Square Roots with the Quotient Rule

You can use the quotient rule to solve radical expressions, like this.

Simplify:


null


We can't take the square root of either of these numbers, but we can use the quotient rule to simplify the expression.


null


75 divided by 3 is 25, which we can take the square root of.


null


Let's try another one.

Simplify:


null


We can use the quotient rule to simply this expression.


null


x3 divided by x is x2.

We can take the square root of x2.


null


And x is the answer.

Rationalize the Denominator

There are occasions when you will simplify a fraction with a radical and still end up with a square root in the denominator. When this happens, there is one more step you will have to do to complete the problem, and that is rationalize the denominator.

Simplify:


null


The first step is to use the quotient rule to make one fraction under the square root symbol.


null


We can simplify this fraction because both numbers are divisible by 3. This reduces the fraction to 5/2. Since there is still a fraction under the radical symbol, we must rationalize the denominator to fully simplify the expression.

To do this, first return the expression to a division problem containing two square roots using the quotient rule.


null


Now you need to multiply the numerator and denominator of the fraction by a number that will eliminate the radical in the denominator of the fraction. Remember, multiplying both the numerator and denominator of a fraction by the same number is like multiplying by 1, so you're not really changing the fraction. For this example, the number to multiply by is the square root of 2.


null


When you do this, you get:


null


Since the square root of 4 is 2, we can simplify one more step, leaving the answer without a radical in the denominator.


null


Let's try one more example.

Simplify:


null


To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support