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and
If a square measures 4
inches on each side, how
would you find its area?
4 inches
4 inches
4 inches
4 inches
We will:
• Understand the meaning of squaring a
number and finding the square root of a
number
• Find squares of numbers
• Raise a whole number to a whole number
power
• Find square roots of perfect squares
• Find approximate square roots of nonperfect squares
Why do we need to be able
to square and find the root
of a number?
• Squares and square roots are used in
the Pythagorean Theorem
• Squares and square roots are used
frequently in Algebra
Remember how to
calculate the area?
4 inches
4 inches
A=l•w
A = 4 in. • 4 in.
2
A = 16 in.
A square must have the
same length and width.
4 inches
4 inches
A=l•w
A = 4 in. • 4 in.
To square a number means to
multiply it by itself.
5 squared means 5 x 5
Take the number 5
And square it!
There is a shorter way to
write 5 x 5.
Say:
“5 squared” or
“5 to the 2nd power”.
These are the parts.
This is the
base
This is the
exponent
What are exponents?
Remember multiplication is repeated
addition:
4x5=4+4+4+4+4
Exponents are repeated
multiplication:
45 = 4 x 4 x 4 x 4 x 4
What do the parts mean?
Tells you how
many...
=5x5x5x5
Tells you what to
multiply...
Evaluate it!
=5x5x5x5
A. 20
B. 625
This is another formula for
finding the area of a square.
s
A=s
2
s is the side
length
Evaluate it!
A. 14
B. 49
Radicals (also called roots) are
directly related to exponents.
The symbol used to indicate a
root is the radical symbol -
Every radical expression has
Radical
three parts…
Index
2
49
Radicand
The square root of 49 could
2
be written as 49 …
but is normally written as 49 .
What does square root mean?
The square root of a number is another
number which when multiplied by itself
gives back the original number.
What is a square root?
?
the measure of the
side of the square
16 = 4
What is the square root
of 36?
36 = 6
Example:
49  7
because
7  7  7  49
2
Also
49   7 because  7  7    7   49
2
These numbers are called
perfect squares
If a number is a perfect square, then you
can find its exact square root.
A perfect square is simply a number that
can be written as the square of another
number.
What are the first 10 whole numbers
that are perfect squares?
2
2
2
2
2
2
2
2
2
1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
2
Not all numbers have an exact
square root as in the previous
examples.
What if you are asked to
find the square root of a
non-perfect square?
Find the two closest perfect
squares.
9 =3
The square root of 15
must be between 3 and 4,
closer to 4.
16 = 4
20 would be between
which two whole numbers?
16 = 4
Between
4 and 5
20
25 = 5
Use the next process to find
a close approximation for
the square root of 10.
Is 10 a perfect square?
Can you make a square out of
these ten tiles?
Is 10 a perfect square?
Can you make a square out of
these ten tiles?
Can we approximate (get close
to) the square root of 10?
You have to make a square
out of the ten tiles
Can we approximate (get close
to) the square root of 10?
close !
What is the length of each
side?
1
36
Is
a good
approximation of 10 ?
1
36
= 3.1666666666666...
10  3.1622776601683...
Most standardized tests
only ask for approximations
like this:
153 is between which of the following
consecutive whole numbers?
A. 15 and 16
C. 12 and 13
B. 9 and 10
D. 76 and 77
1. A student earned a grade of 80% on a math test that had 20
problems. How many problems on this test did the student
answer correctly?
2. A metal bar weighs 8.15 ounces. 93% of the bar is silver.
How many ounces of silver are in the bar?
3. Cost of sled: $99.50
Markup: 95%
Find the selling price.
4. Cost of a comic book: $3.95
Markup: 20%
Find the selling price.
Quiz
2
1. Evaluate 7
49
2. Evaluate 144
12
3
3. Evaluate 3
27
4. 200 is between what
two consecutive whole
14 and 15
numbers?