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Fun with
Radicals
More Fun
with Radicals
Exciting Extra Exciting
Exponents
Exponents
Scientific
Pot Luck
Q $100
Q $100
Q $100
Q $100
Q $100
Q $200
Q $200
Q $200
Q $200
Q $200
Q $300
Q $300
Q $300
Q $300
Q $300
Q $400
Q $400
Q $400
Q $400
Q $400
Q $500
Q $500
Q $500
Q $500
Q $500
Final Jeopardy
$100 Question Fun with
Radicals
What is the simplified answer for
6 2 6
$100 Answer Fun with Radicals
2 6 2
Add the coefficient of like radicals
$200 Question Fun with
Radicals
What is the simplified answer for
5 3 9 3
$200 Answer Fun with Radicals
4 3
Subtract coefficient of like radicals
$300 Question Fun with
Radicals
What is the simplified answer for
5
7
$300 Answer Fun with Radicals
35
Multiply the radicands and simplify if possible
$400 Question Fun with
Radicals
What is the simplified answer for
7
3
$400 Answer Fun with Radicals
21
3
Multiply by the “special 1”
simplify if possible
3
3 , then
$500 Question Fun with
Radicals
Graph the point
5 on the number line.
$500 Answer Fun with Radicals

1
2
3
4
5 Is between 4 and 9 , so it’s square root is
between the square roots of those numbers, 2 and 3
$100 Question More Fun with
Radicals
Solve
121
$100 Answer More Fun with
Radicals
11
We are looking for the positive square root
of the perfect square, 121
$200 Question More Fun with
Radicals
Estimate the  227
$200 Answer More Fun with
Radicals
About 15.2
It falls between the perfect squares 225
and 256, so it’s square root is between 15
and 16. Since 227 is closest to 225, it’s
square root is also closer to 15 than 16.
$300 Question More Fun with
Radicals
Identify each of the radicals as
rational or irrational
45
10
49
100
$300 Answer More Fun with
Radicals
45
10
49
100
Irrational, They are not perfect
squares so cannot simplify to a
number that can be a fraction
Rational They are perfect
squares so simplify to the
integers 7 and 10. Both 7 and 10
can be written as fractions.
$400 Question More Fun with
Radicals
Simplify
5 10
$400 Answer More Fun with
Radicals
50  25  2  25
2 5 2
Multiply the radicands, then simplify by finding perfect square factors.
$500 Question More Fun with
Radicals
Combine
4 3 6 3
$500 Answer More Fun with
Radicals
2 3
Since we have like radicands, we can subtract the coefficients
$100 Question Exciting
Exponents
Simplify
1
3
$100 Answer Exciting
Exponents
1
3
The negative exponent is simplified by moving it’s base
to the other side of the fraction bar and making it a positive exponent.
We put a 1 in the numerator as a place holder.
$200 Question Exciting
Exponents
Evaluate
3
3
2
4
$200 Answer Exciting
Exponents
1. Make the exponents “happy”
by moving their bases to the
other side of the fraction bar.
2. Simplify by
multiplying the base by
itself according to the
exponent
42
33
4 4 16

3 3 3 27
$300 Question Exciting
Exponents
Evaluate
2
3
3 3
$300 Answer Exciting
Exponents
1.
Same base so we can Subtract the exponent.
(  2   3)
3
3 3
1
Remember, any number to the
first power is always itself.
$400 Question Exciting
Exponents
Evaluate
6
10
6
8
$400 Answer Exciting
Exponents
1. Same base so we can add the exponents.
6
( 10 8)
6
2
2. Now we must simplify; get rid of that negative exponent.
Move the base to the other side of the fraction bar and make
the exponent positive “happy”.
1
62
3. Finally, multiply the base by itself to finish simplifying.
1
1

6 6 36
$500 Question Exciting
Exponents
Evaluate
3
1
2
4
$500 Answer Exciting
Exponents
1. Simplify the negative exponent by moving its base
to the other side of the fraction bar and make the exponent positive.
Remember, 21 = 2.
3 1

4 2
2. Now, find common denominators and add the fractions.
3 2 5
1
  1
4 4 4
4
$100 Question Extra Exciting
Exponents
What is the simplified answer for
5
6 1
8x y z
$100 Answer Extra Exciting
Exponents
Move bases with negative exponents to the
other side of the fraction bar and make the
exponents positive, “happy”.
Bases with positive exponents stay where they
are!!
5
6 1
8x y z
6
8y
5 1
xz
$200 Question Extra Exciting
Exponents
What is the simplified answer for
24 x 5 y 1
3
6x
$200 Answer Extra Exciting
Exponents
24
4
1. The fraction 6 reduces to 1
2. Move bases with negative exponents to the other side of the fraction
bar and make the exponents positive, “happy”.
Bases with positive exponents stay where they are!!
5
4x y
1x 3
1

4 x3
6 x5 y1
x3
2

x
3. Subtract exponents for x5
so we have to move that x base to the other
side of the fraction bar for our final answer.
4
2
x y
$300 Question Extra Exciting
Exponents
What is…
6
When x=2 ?
( x 5)
$300 Answer Extra Exciting
Exponents
1. Substitute 2 for the variable x and simplify the exponent.
6
(2  5)
6
3
2. Now we have a negative exponent so we have to move its
base to the other side of the fraction bar and make the exponent
positive.
1
63
3. Multiply the base 6 by itself 3 times.
1
1

6 6 6 216
$400 Question Extra Exciting
Exponents
Simplify
3
4
4 (4 )
$400 Answer Extra Exciting
Exponents
Remember, parentheses are another way of saying multiply.
1. Bases are the same, so we can add the exponents.
4
( 3 4)
4
1
2. Since any number to the power of 1 is itself, the answer is…
4
$500 Question Extra Exciting
Exponents
Simplify the Expressions
(1)
1
2
1
8
0
5 5
7
7
$500 Answer Extra Exciting
Exponents
(1)
1
1
 1  1
1
2
1
1
1
2
1
8
5 5
0
1
7
7
(7  7)
5
5
1
0
$100 Question Scientific Pot
Luck
Simplify
5
10
$100 Answer Scientific Pot Luck
Step 1 – simplify the fraction
Now that we simplified the
fraction, we multiply by the
“special 1”
5
5
1
1



10
2
10
2
1
2
2
2

2
2
$200 Question Scientific Pot
Luck
What is 8.6 x 10-3 in standard notation?
$200 Answer Scientific Pot Luck
Move the decimal to the left 3 spaces (exponent tells you how far to
move and which direction)
8.6 x 10-3
0.0086
$300 Question Scientific Pot
Luck
What is the product of 80,000 and 90
written in scientific notation
$300 Answer Scientific Pot Luck
Move the decimal to the left until just 1 digit is to
it’s left. Your exponent will be the number of
decimal hops.
7 2 0 0 0 0 0= 7.2 x 106
$400 Question Scientific Pot
Luck
Simplify the quotient and write
the answer in scientific notation
(9 x 107)  (3 x 104)
$400 Answer Scientific Pot Luck
Subtract exponents 7-4=3
(9 x 107)  (3 x 104)
Divide 9  3 = 3
(3 x 103)
$500 Question Scientific Pot
Luck
How much greater is 9.4 x 103 than 7.5 x 10-2
$500 Answer Scientific Pot Luck
2 methods to solve.
1.
Adjust one of the numbers so the exponents are the same. Remember
LARS when moving the decimal and changing the exponent.
2.
Change both numbers to standard notation. Subtract. Then, change the
difference back to scientific notation. (I find this one easier unless the
exponents are extremely big.)
9400.000
-
3.
Adjust to scientific notation
.075
9399.925
9.39925 x 103
Final Jeopardy
How are you going to study
for the math test tonight?
Final Jeopardy Answer
1. Review notes and practice problems from
the unit.
2. Work out all the problems from the study
guide and check my answers to the key I
now know is correct.