April 28, 2016
Warm-up Problem: April 11, 2016.
A perfect square is a number whose square
root is an integer. If a number is not a perfect
square, its square root is an irrational number
n
1
2
3
n2
1
4
9
8
9
10 11 12 13 14 15
4
5
6
7
16 25 36 49
64 81 100 121 144 169 196 225
16 17 18 19 20 21 22 23
256 289 324 361 400 441 484 529
24 25 26 27 28 29 30 40
576 625 676 729 784 841 900 1600
1
April 28, 2016
Warm-up Problem: April 11, 2016.
A perfect cube is a number whose cube root
is an integer. If a number is not a perfect cube,
its cube root is an irrational number.
n
1
2
3
4
n3
1
8
27
64 125 216 343
8
9
5
6
7
10 11 12 13 14 15
512 729 1000 1331 1728 2197 2744 3375
2
April 28, 2016
Warm-up Problems: April 12, 2016.
What is the index of the radical above? 5
What is the radicand of the radical above?
15 5 10
The radicand is 32x y z
.
Simplify the radical.
Consider
What can we do to make this true?
Make it
If the index of a radical is even and the radicand
contains a variable raised to an even power, the
result must have absolute values if power of the
variable is odd. In all other cases, no absolute
values should be included in the answer.
3
4
3
x =x
4
x =x
4
x = |x|
2
3
April 28, 2016
Warm-up Problems: April 13, 2016.
4
April 28, 2016
Warm-up Problems: April 14, 2016.
Simplify each. Assume that variables represent
nonnegative values.
Simplify each. Assume that variables represent
any real values.
What is the domain of this function?
5
April 28, 2016
Warm-up Problems: April 15, 2016.
1. Find the square roots of 196.
The square roots of 196 are ±14.
2. Evaluate each.
2 3
= -9
= 21
= 4x y
3. Write in exponential form.
= 2x
5/3 5
z
-2
4
-8
= (5y ) = 625y
4. Use the rules of exponents to simplify each.
2 19/3
= -6x y
6
April 28, 2016
Warm-up Problem: April 18, 2016.
7
April 28, 2016
Warm-up Problems: April 19, 2016.
±72
-11
21.21
3
3
0.2|x |y √y
√9x y
4 10
9
2 5
=3x y
7 1/3
(8x yz ) =2x3y1/3z7/3
9x
4/5
•6x
4/3
=54x
32/15
8
April 28, 2016
Warm-up Problems: April 21, 2016.
9
April 28, 2016
Warm-up Problems: April 22, 2016.
10
April 28, 2016
Warm-up Problems: April 25, 2016.
Simplify each.
11
April 28, 2016
Warm-up Problems: April 26, 2016.
Rationalize each denominator and simplify.
12
April 28, 2016
Warm-up Problems: April 27, 2016.
Solve each equation.
13
April 28, 2016
Warm-up Problems: April 28, 2016.
Simplify each.
14
April 28, 2016
Simplify each.
Solve each.
15