Download EX: 16 4

Name: ____________________________________________ Date: ____________________ Period: ________
We Will Learn To: __________________________________________________________________________
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Numbers like 1, 4, 9, 16, 25, etc. are called ______________________________ because they are the
product of an integer times itself.
o EX: 4 × 4 or 42 = 16
When you take the square root of a perfect square, the result is a ______________________________.
o EX :
16  4
Background Vocabulary:
_______________
Steps to Simplify Radicals:
1. Find the largest ________________________________________, excluding 1.
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Note: A factor is a number that divides evenly into a given number with no remainder.
2. Write the number as the _______________ of the perfect square factor and its other factor.
3. Split each factor into two separate _______________.
4. Simplify the ______________________________ radical.
Example 1: Write
75 in most simplified form.
Example 2: Simplify
24  3
Discussion Questions:
1. What happens if you do not use the largest perfect square factor when simplifying?
2. What if the number under the radical does not have any perfect square factors other than 1?
Example 3: Rationalizing the Denominator
16
3
1. Separate the numerator and denominator into
separate radicals.
Example 4: Rationalizing the Denominator
27
2
2. Simplify each radical if possible.
3. Multiply both the numerator and denominator by
the root.
4. Simplify.
Independent Practice: Simplify each radical. If the radical is in simplest form write ‘Cannot be simplified’.
1.
4.
28
6
2
2.
42
3.
8  10
5.
64
10
6.
18
5
7. Find the distance between D(0, 4) and F(3, -2). Write your answer in simplest radical form.