Transcript • DO NOW: SOLVE THE INEQUALITY BY FOLLOWING THE STEPS WE HAVE LEARNED OVER THE LAST TWO DAYS. THEN WE WILL GRAPH TOGETHER.

• DO NOW: SOLVE THE INEQUALITY BY
FOLLOWING THE STEPS WE HAVE
LEARNED OVER THE LAST TWO DAYS.
THEN WE WILL GRAPH TOGETHER ON THE
CALCULATOR;
X  6 X  1  13
2
HOW DO WE SIMPLIFY
RADICALS?
1. simplify square roots, and
2. simplify radical expressions.
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
6. Use a calculator to find each
square root. Round the decimal
answer to the nearest hundredth.
 46.5
6.82, -6.82
What numbers are perfect squares?
1•1=1
2•2=4
3•3=9
4 • 4 = 16
5 • 5 = 25
6 • 6 = 36
49, 64, 81, 100, 121, 144, ...
1. Simplify
147
Find a perfect square that goes into 147.
147  49 3
147  49
147  7 3
3
2. Simplify 605
Find a perfect square that goes into 605.
121 5
121 5
11 5
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.
49 x
7x
2
5. Simplify 8x
25
4 2x
12
2x 2x
25
Simplify
1.
2.
3.
4.
3x6
3x18
6
9x
18
9x
9x
36
What are Perfect Cubes?
•
•
•
•
•
•
13 = 1 x 1 x 1 = 1
23 = 2 x 2 x 2 = 8
33 = 3 x 3 x 3 = 27
43 = 4 x 4 x 4 = 64
53 = 5 x 5 x 5 = 125
and so on and on and on…..
2x2=4
2
2
3x3=9
3
3
4 x 4 = 16
4
4
5 x 5 = 25
5
5
The square root of 4 is
2
The square root of 9 is
3
The square root of 16 is
4
The square root of 25 is
5
Cubes
5
7
6
8
1
3
2
4
2x2x2=8
2
2
2
3 x 3 x 3 = 27
NTH ROOTS
• a square (second) root
is written as:
• a cube (third) root is
written as:
• a fourth root is written
as:
• a fifth root is written
as:
3
4
5
n
SIMPLIFY
1.
3
343
2.
3
8
3.
3
3
27 x y
6
ANSWERS
• 1. 7
• 2. -2
• 3. 3xy2
• CUBES:
Cathy is building a cubic
storage room. She wants the volume of
the space to be 1728 cubic feet. What
should the dimensions of the cube be?
ASTRONOMY A special form of
Kepler’s Third Law of Planetary Motion
is given by a  3 P2 where a is the
average distance of an object from the
Sun in AU (astronomical units) and P is
the period of the orbit in years. If an
object is orbiting the Sun with a period
of 12 years, what is its distance from
the Sun?
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