Transcript Simplify Radicals - nemsgoldeneagles

Objectives
The student will be able to:
1. simplify square roots, and
2. simplify radical expressions.
Designed by Skip Tyler, Varina High School
If x2 = y then x is a square root of y.
In the expression 64 ,
is the radical sign and
64 is the radicand.
1. Find the square root: 64
8
2. Find the square root: - 0.04
-0.2
3. Find the square root: ± 121
11, -11
4. Find the square root:
21
5. Find the square root:
5

9
441
25
81
What is a Perfect Square?
It is a number that has a whole
number square root.
What numbers are perfect squares?
1
4
9
16
25
36
49, 64, 81, 100, 121, 144, ...
1. Simplify
147
Find a perfect square that goes into 147.
147 = 49i3
147 = 49i 3
147  7 3
The square root is simplified when
there are no perfect squares left in
the radicand.
What are some strategies for finding the
perfect squares in radicands?
2. Simplify
605
Find a perfect square that goes into 605.
121i5
121i 5
11 5
Compare and Contrast
Find the square root of
calculator.
972 with your
31.18
This means
31 and 0.18
Now simplify the square root of
This means 18
times 3
972
18 3
Are these answers equivalent?
Simplify
1.
2.
3.
4.
2 18
.
3 8
6 2
36 2
.
.
.
72
How do you simplify variables in the radical?
x
7
Look at these examples and try to find the pattern…
x  x
2
x x
3
x x x
4
2
x x
5
2
x x x
6
3
x x
1
What is the answer to
x x
7
3
x ?
7
x
As a general rule, divide the
exponent by two. The
remainder stays in the
radical.
4. Simplify 49x
2
Find a perfect square that goes into 49.
49i x
7x
2
5. Simplify 8x
4i2x
12
2x
25
2x
25
Simplify
1.
2.
3.
4.
3x6
3x18
6
9x
18
9x
9x
36
6. Simplify 6 · 10
Multiply the radicals.
60
4i15
4i 15
2 15
7. Simplify 2 14 · 3 21
Multiply the coefficients and radicals.
6 294
6 49i6
6i 49i 6
6i7i 6
42 6
Simplify
1.
2.
3.
4.
4x
.
2
3
4
4 3x
2
x 48
4
48x
.
.
.
3
6x i 8x
How do you know when a radical
problem is done?
1. No perfect squares are in the radicand.
Example:
8
2. There are no fractions in the radical.
1
Example:
4
3. There are no radicals in the denominator.
Example:
1
5
Simplify.
Whew! It
simplified!
108
3
Divide the radicals.
108
3
36
6
Uh oh…
There is a
radical in the
denominator!
Simplify.
294
6
Divide the radicals.
Whew! It
simplified!
294
6
49
7
Uh oh…
There is a
radical in the
denominator!
Simplify.
200
5
Divide the radicals.
200
4
40
4·10
2 10
Simplify
8 2
2 8
4 1
4
Whew! It simplified
again! I hope they
all are like this!
4
2
2
Uh oh…
Another
radical in the
denominator!
Simplify 5 80
3 5
5 80
= ·
3
5
5 80
·
3
5
5
· 16
3
5 4
·
3 1
20
=
3
5
7
Simplify
Uh oh…
There is a
fraction in
the radical!
Since the fraction doesn’t reduce, split the radical up.
5
7
=
How do I get rid
of the radical in
the denominator?
5
7
i
7
7
35

49
Multiply by the same square
root to make the denominator
a perfect square!
35

7
Simplify
25
3
i
3
3
=
25
3
=
75
25·3
=
3
9
25
3
Multiply by the same square
root to make the denominator
a perfect square!
5 3
=
3
3
Simplify
12
in two different ways.
Describe which way you prefer
and explain why.
3
2
Closure:
Explain how you can tell if a
radical expression is in
simplified form.