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](images/simplify-radicals/picture-of-radicand.png)
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](images/dividing-radicals/dividing-square-roots-rule.gif)
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.
![Rule with numbers](images/dividing-radicals/rule-with-numbers.gif)
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 1Combine square roots under 1 radicand.
![Dividing Square roots example](images/dividing-radicals/example-1/example-1-step-1.gif)
Divide (if possible). Since 150 is divisible by 2, we can do this.
![Example 1, step 2](images/dividing-radicals/example-1/example-1-step2.gif)
Simplify the radical (if possible)
![Example 1, step 3](images/dividing-radicals/example-1/example-1-step-3.gif)
Example 2
![Example 1-dividing square roots easy](images/dividing-radicals/example-2/example-2.gif)
Rewrite the expression by combining the rational andirrational numbers into two distinct quotients.
![Dividing Square roots example](images/dividing-radicals/example-2/example-2-step1.gif)
Combine the square roots under 1 radicand.
![Example 2, step 2](images/dividing-radicals/example-2/example-2-step2.gif)
Divide the square roots and the rational numbers.
![Example 2, step 3](images/dividing-radicals/example-2/example-2-step3.gif)
Simplify the radical (if possible)
![Example 2, step 4](images/dividing-radicals/example-2/example-2-step4.gif)
Practice Dividing Square Roots
Directions: Divide the square roots and express your answer insimplest radical form
Problem 1
Divide (if possible). Since 200 is divisible by 10, we can do this.
![Problem 1, step 2](images/dividing-radicals/problem-1/problem-1-step-2.gif)
Problem 2
Divide (if possible). Since 140 is divisible by 5, we can do this.
![Problem 2, step 2](images/dividing-radicals/problem-3/problem-3-ste2.gif)
Problem 3
This problem is like example 2.
Step 1Rewrite the expression by combining the rational andirrational numbers into two distinct quotients.
![Dividing Square roots example](images/dividing-radicals/problem-4/problem-4-step1.gif)
Combine the square roots under 1 radicand.
![Problem 3, step 2](images/dividing-radicals/problem-4/problem-4-step2.gif)
Divide the square roots and the rational numbers.
![Problem 3, step 3](images/dividing-radicals/problem-4/problem-4-step3.gif)
Problem 4
This problem is like example 2.
Step 1Rewrite the expression by combining the rational and irrational numbers into two distinct quotients.
![Problem 4, step 1](images/dividing-radicals/problem-5/problem-5-step1.gif)
Combine the square roots under 1 radicand.
![Problem 4, missing step](images/dividing-radicals/problem-5/problem-5-mising-step.gif)
Divide the square roots and the rational numbers.
![Problem 4, step 2](images/dividing-radicals/problem-5/problem-5-step2.gif)