How To Divide Radicals - Kate's Math Lessons

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Dividing Radicals

Accompanying Resource: Dividing Radical Expressions Boom Cards Dividing Radicals Digital Boom Cards - great algebra activity for distance learning!

​How Do You Divide Radicals?

When you're multiplying radicals together, you can combine the two into one radical expression. There's a similar rule for dividing two radical expressions. If you have one square root divided by another square root, you can combine them together with division inside one square root. Rule for dividing radical expressions. This property can be used to combine two radicals into one. It can also be used the other way around to split a radical into two if there's a fraction inside.Important NoteNotice that it says b cannot equal 0. This is because b is in the denominator and you can't divide by 0! An expression with 0 in the denominator is undefined. Think of the word NO to help you remember. Dividing by 0. No! Don't do it! What about 0 in the numerator? It's OK to have a 0 in the top of a fraction. 0 divided by any nonnegative number is just 0. It's OK to have 0 in the numerator of a fraction.

Example 1

Simplify. How do you divide two radical expressions? To divide two radicals, you can first rewrite the problem as one radical. The two numbers inside the square roots can be combined as a fraction inside just one square root. Once you do this, you can simplify the fraction inside and then take the square root. 		Kate's Math Lessons Welcome to Kate's Math Lessons! Teachers: don't miss the study guides and activities that go with the lessons! Picture
How to simplify an expression with division of radicals.

Example 2

Simplify. How do you simplify a fraction with square roots? First, combine into one radical. Then simplify what's inside. Don't forget to look for factors that are perfect squares. If you need help with this step, make sure to check out the lesson on simplifying radicals. How to simplify fractions with radicals.

​Example 3

Simplify for x>0. How do you simplify radicals with fractions? ​First, combine into one radical. Then simplify the fraction on the inside. Make sure to continue simplifying until there aren't factors left that are perfect squares. How do you divide radical expressions with variables?

Practice

Now that you've learned how to divide radicals, are you ready to try some problems on your own? Click the START button below to take a practice quiz.
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Tag » How To Divide Square Roots