Square and sq root
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![Page 1: Square and sq root](https://reader036.fdocuments.in/reader036/viewer/2022081508/5579e47fd8b42aa54d8b4ce8/html5/thumbnails/1.jpg)
and
Square
sSquare
s
Square Roots
Square Roots
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If a square measures 4 inches on each side, how would you find its area?
4 inches4
inch
es 4
inch
es
4 inches
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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
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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
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Remember how to calculate the area?
4 inches A = l •
w A = 4 in. • 4 in. 4
in
ches
A = 16 in.2
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A square must have the same length and
width. 4 inches
A = l • w A = 4 in. • 4 in.
4
inch
es
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To square a number means to multiply it by
itself.
5 squared means 5 x 5
Take the number 5
And square it!
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There is a shorter way to write 5 x 5.
Say:“5 squared” or
“5 to the 2nd power”.
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These are the parts.
This is the base
This is the exponent
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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
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What do the parts mean?
Tells you what to multiply...
Tells you how many...
= 5 x5 x 5 x 5
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Evaluate it!
= 5 x5 x 5 x 5
B. 625A. 20
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This is another formula for finding the area of a
square.
sA = s
2
s is the side length
![Page 14: Square and sq root](https://reader036.fdocuments.in/reader036/viewer/2022081508/5579e47fd8b42aa54d8b4ce8/html5/thumbnails/14.jpg)
Evaluate it!
B. 49A. 14
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Try these:
NumberSquared
Factors StandardForm
92
11119
102
9 9 81112 12132 3 3
10 10
100
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Radicals (also called roots) are directly related to exponents.
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The simplest type of radical is a square root.
Radicals beyond square roots exist, but we will not explore them here.
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The rules for radicals that you will learn work for all radicals – not just square roots.
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The symbol used to indicate a root is the radical symbol -
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Every radical expression has three parts…
• Radical symbol• Index• Radicand
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Every radical expression has three parts…
Index
Radicand
Radical
2 49
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The index of a radical is a whole number greater than or equal to 2.
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The index of a square root is always 2.
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but is normally written as .
The square root of 49 could be written as …2 49
49
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What does square root mean?
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The square root of a number is another number which when multiplied by itself gives back the original number.
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What is a square root?
the measure of the side of the square
16 = 4
?
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What is the square root of 36?
36 =6
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49777 2
Example:
because
Also
because
749
749 49777 2
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These numbers are called perfect squares
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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.
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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
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Not all numbers have an exact square root as in the previous examples.
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What if you are asked to find the square root of a
non-perfect square?
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Find the two closest perfect squares.
16 = 4
The square root of 15 must be between 3 and 4, closer to 4.
9 = 3
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20 would be between which two whole
numbers?
25 = 5
16 = 4
20Between 4 and 5
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Use the next process to find a close approximation for the square root of 10.
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Is 10 a perfect square?
Can you make a square out of these ten tiles?
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Is 10 a perfect square?
Can you make a square out of these ten tiles?
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Can we approximate (get close to) the square root of
10?
You have to make a square out of the ten tiles
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What is the length of each side?
close !
Can we approximate (get close to) the square root of
10?
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16
Is 3 a good approximation of 10
?
163
= 3.1666666666666... 3.1622776601683...10
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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
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QuizQuiz1. Evaluate 72 2.Evaluate 1443.Evaluate 33
4. 200 is between what two consecutive whole numbers?
491227
14 and 15