Vocabulary Refresher
The radicand refers to the number under the radical sign. In the radical below, the radicand is the number '5'.
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;)
When you divide two square roots you can "put" both the numerator and denominator inside the same square root. Below is an elink 1xample of this rule using numbers.
As you can see the '23' and the '2' can be rewritten inside the same radical sign.
Examples of Dividing Square Roots
Example 1
$ \frac{ \sqrt{150 }}{ \sqrt 2} $
Step 1
Combine square roots under 1 radicand.
Divide (if possible). Since 150 is divisible by 2, we can do this.
Simplify the radical (if possible)
Example 2
Step 1
Rewrite the expression by combining the rational andirrational numbers into two distinct quotients.
Combine the square roots under 1 radicand.
Divide the square roots and the rational numbers.
Simplify the radical (if possible)
Practice Dividing Square Roots
Directions: Divide the square roots and express your answer insimplest radical form
Problem 1
Step 2
![Problem 1, step 2]()
Divide (if possible). Since 200 is divisible by 10, we can do this.
Step 3
Problem 2
Step 2
![Problem 2, step 2]()
Divide (if possible). Since 140 is divisible by 5, we can do this.
Step 3
Problem 3
This problem is like example 2.
Step 1Rewrite the expression by combining the rational andirrational numbers into two distinct quotients.
Step 2
![Problem 3, step 2]()
Combine the square roots under 1 radicand.
Step 3
![Problem 3, step 3]()
Divide the square roots and the rational numbers.
Step 4
Problem 4
This problem is like example 2.
Step 1Rewrite the expression by combining the rational and irrational numbers into two distinct quotients.
Step 2
![Problem 4, missing step]()
Combine the square roots under 1 radicand.
Step 3
![Problem 4, step 2]()
Divide the square roots and the rational numbers.
Step 4
