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Square
sSquare
s
Square Roots
Square Roots
If a square measures 4 inches on each side, how would you find its area?
4 inches4
inch
es 4
inch
es
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 non-
perfect 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 A = l •
w A = 4 in. • 4 in. 4
in
ches
A = 16 in.2
A square must have the same length and
width. 4 inches
A = l • w A = 4 in. • 4 in.
4
inch
es
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:
Exponents are repeated multiplication:
4 x 5 = 4 + 4 + 4 + 4 + 4
45 = 4 x 4 x 4 x 4 x 4
What do the parts mean?
Tells you what to multiply...
Tells you how many...
= 5 x5 x 5 x 5
Evaluate it!
= 5 x5 x 5 x 5
B. 625A. 20
This is another formula for finding the area of a
square.
sA = s
2
s is the side length
Evaluate it!
B. 49A. 14
Try these:
NumberSquared
Factors StandardForm
92
11119
102
9 9 81112 12132 3 3
10 10
100
Radicals (also called roots) are directly related to exponents.
The simplest type of radical is a square root.
Radicals beyond square roots exist, but we will not explore them here.
The rules for radicals that you will learn work for all radicals – not just square roots.
The symbol used to indicate a root is the radical symbol -
Every radical expression has three parts…
• Radical symbol• Index• Radicand
Every radical expression has three parts…
Index
Radicand
Radical
2 49
The index of a radical is a whole number greater than or equal to 2.
The index of a square root is always 2.
but is normally written as .
The square root of 49 could be written as …2 49
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
49777 2
Example:
because
Also
because
749
749 49777 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?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
2222222222 10,9,8,7,6,5,4,3,2,1
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.
16 = 4
The square root of 15 must be between 3 and 4, closer to 4.
9 = 3
20 would be between which two whole
numbers?
25 = 5
16 = 4
20Between 4 and 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
What is the length of each side?
close !
Can we approximate (get close to) the square root of
10?
16
Is 3 a good approximation of 10
?
163
= 3.1666666666666... 3.1622776601683...10
Most standardized tests only ask for
approximations like this:
153 is between which of the following consecutive whole numbers?
A. 15 and 16
B. 9 and 10
C. 12 and 13
D. 76 and 77
QuizQuiz1. Evaluate 72 2.Evaluate 1443.Evaluate 33
4. 200 is between what two consecutive whole numbers?
491227
14 and 15
