Upload
clarissa-griffith
View
243
Download
4
Tags:
Embed Size (px)
Citation preview
Simplifying Radicals
Section 5.3
Radicals Definition Simplifying Adding/Subtracting Multiplying Dividing Rationalizing the denominator
Radicals - definitions
The definition of is the number that when multiplied by itself 2 times is x.
x
2224 xxxx 2
16
Simplifying radicals
Most numbers are not perfect squares, but may have a factor(s) that is (are) a perfect square(s).
The perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ….
Try these - simplify:
If a radical has a perfect square factor, then we can pull it out from under the sign.
Ex:
98724832
50 225 25 25
745 bax
3 3 727m n
Adding or Subtracting Radicals
24232
24232182
To add or subtract square roots you must have like radicands (the number under the radical).
Sometimes you must simplify first:
Try These
5553 5553
48753 803202
18554
Multiplying Radicals
62343232
10152553
572 10253 2
2
You can multiply any square roots together. Multiply any whole numbers together and then multiply the numbers under the radical and reduce.
Try these:
)32)(123( 2
52
Dividing Radicals
To divide square roots, divide any whole numbers and then divide the radicals one of two ways:
1) divide the numbers under the radical sign and then take the root, OR
2) take the root and then divide. Be sure to simplify.
5
20
5
20
25
52
5
20 24
5
20 or
Try These
4
1
10
40
4
100
22
148
25
100
10
80
Rationalizing Radicals
It is good practice to eliminate radicals from the denominator of an expression.
For example:
We do not want to change the value of the expression, so we need to multiply the fraction by 1. But “1” can be written in many ways…
2
3 2
222 2
21
2
23
22
23
2
2
2
3
We need to eliminate
Since we will multiply by one where
Try These
3
5
5
22
10
53
12
35
83
52
20
7