Transcript Finding Slope – Intercept Form From Points

Simplifying Radicals
Unit VIII, Lesson 4
Online Algebra
VHS@PWCS
Square Root Review
Find the principal square root of each of the
following.
1.
2.
3.
81
25
125
4
1. 9
2. 5
3. About 11.8
4. About 14.1
200
Square Root Review
Recall from lesson VIII.3 that a square root is
defined as:
If a2 = b, then a is a square root of b.
So far we have used the decimal form of any
square root that is not a perfect square (a
number that as a whole number for a square
root). Now we will leave our square roots in
radical form.
Radical Form
When you are asked to leave an answer in
radical form, it means to leave any
square roots in your answer.
Examples:
4 5
13 2
10 15
Radical Form
There are some rules we have to following when
simplifying radicals. A radical is in simplest
form if the following is true:
1.
2.
3.
All numbers under the square root symbol
have no perfect square factors.
The expression under the radical does not
contain fractions.
The denominator does not contain a radical
expression.
What does all this mean. Click to find out!
Simplifying radicals
Simplify
125
Our first rule says that we can not have numbers with a perfect square
factor under the radical sign.
125 has a factor of 25. Factors are numbers that divide the product
without a remainder.
25 x 5 = 125
We can rewrite 125 as 25  5
Since
25  5 , we can write 125 as 5 5
Simplifying Radicals
That probably sounded difficult, but it is pretty easy when
broken down. To find the square root of 45.
1.
2.
45  3 3 5
45
9
3
3.
5
3
Find all the prime factors of 45. I use a factor tree.
Rewrite using the prime factors
Pull out pairs of factors. In this case the 3’s.
3 5
Though we have pulled out pairs we only use one 3 in our
answer, because 3(3) is 9 and the square root of 9 is 3.
The only factors of 5 are 1 and 5 so the only perfect square
under the square root symbol is 1 and our square root
is simplified.
Simplifying Radicals

Find all the factors of 240?
Rewrite using the prime factors
240
240  2 2 2 2 3 5

10
Pull out pairs.
2 2 2 2 352 2 35

24
Multiply numbers outside the
radical sign and then those
under the radical sign.
4 15
2
12
5
3
4
2
2
2
Try these on your own. Click
for the answers.
1.
2.
50
300
1. 5 2
2. 10 3
3. 2 7
3.
4.
28
80
4. 4 5
Remember our
first rule: No
perfect square
factors under
the radical sign!
Multiplying square roots.
Multiplication property of square roots
For all a and b greater than or equal to 0:
So to multiply 8 6
1. Find all the factors of 8 and 6.
2.
3.
4.
222 23
Write under one radical.
22223
Pull out all pairs.
22 3
Multiply
4 3
8
4
2
2
2
6
2
3
Multiplying Square Roots – Try
these!
1.
30
6
2.
12
27
3.
4.
14
15
8
35
6 5
2. 18
1.
3.
4 7
4.
5 21
Dividing Square Roots
Our last 2 rules deal with fractions or
dividing square roots.
 The expression under the radical does
not contain fractions.
 The denominator does not contain a
radical expression.
Dividing Square Roots
For any numbers a > 0 and b > 0:
So to simplify
1.
2.
a
a

b
b
25
64
Split in to 2 square roots
25
64
Take the square root of each and simplify. 5
8
Simplify:
96
9
1. Find the each square root.
2. Simplify if needed.
222223
33
22 23
3
4 6
3
Review – Are the following radical
expressions in simplest form?
1.
2.
3.
4.
2 12
5 30
1.
No 12 has 4 as a factor which is a
perfect square.
2.
Yes the factors of 30 are 2, 3, and 5.
None of which are perfect squares.
3.
No there is a radical in the
denominator. The square root of 4 is
2. So our answer is 5/2
4.
No the 2’s can be canceled so our
answer is 3
5
4
2 3
2