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Dividing Square Roots

How to divide square roots--with examples

Vocabulary Refresher
The radicand refers to the number under the radical sign. In the radical below, the radicand is the number '5'.
Picture of radicand
Refresher on an important rule involving dividing square roots:
The rule explained below is a critical part of how we are going to divide square roots so make sure you take a second to brush up on this. (Or learn it for the first time;)
Dividing Square Roots Rule When you divide two square roots you can "put" both the numerator and denominator inside the same square root. Below is an example of this rule using numbers
As you can see the '23' and the '2' can be rewritten inside the same radical sign.
Video on How To Divide Square Roots

Examples of Dividing Square Roots

Example 1
Example 1-dividing square roots easy
Step 1) Combine square roots under 1 radicand Dividing Square roots example
Step 2) Divide (if possible). Since 150 is divisible by 2, we can do this.
Step 3) Simplify the radical (if possible)
Example 2
Example 1-dividing square roots easy
Step 1) Rewrite the expression by combining the rational and irrational numbers into two distinct quotients. Dividing Square roots example
Step 2) Combine the square roots under 1 radicand
Step 3) Divide the square roots and the rational numbers.
Step 4) Simplify the radical (if possible)

Practice Dividing Square Roots

Directions: Divide the square roots and express your answer in simplest radical form
Problem 1)
Step 1
Problem 2)
Step 1
Problem 3)
Step 1
Problem 4)
Step 1