# Examples ```Chapter 1 Test: October 24
Review 3 Previous Study Guides (on website)
Roots (Lesson 8)
Examples:
√64 = 8 (Since 8 x 8 = 64)
−√4 = -2
Don't let the sign out front confuse you! Just find the square root of
the number and bring the sign in front down! What is the square root
of 4? 2 Rewrite the answer with the sign. -2
&plusmn;√1.21 = &plusmn; 1.1
When there's a decimal in the number, look at the number without a
decimal point there.
121. Is there a square root of 121? Yes! = 11
Because there's a decimal in the original number, you're going to have
to put a decimal in the solution. 1.1
Leave the sign on the outside in your solution too. We read that as
&quot;plus or minus.&quot;
T2 = 169
We need to solve this equation. Remember, when solving any equation,
whatever we do to one side, we do to the other. To cancel out
something being “squared” we take the “square root”
√169 = &plusmn;13
T= &plusmn;13
Estimating with Roots (Lesson 9)
Examples:
Estimate √83
We know 83 is not a “perfect square.” This means that no whole
number can be multiplied by itself to get 83. The closest perfect
square less than 83 is 81. The closest perfect square greater than 83
is 100.
√81 = 9
√100 = 10……… so the √83 is between 9 and 10. Since 83 is
closer to 81 than 100 the SQUARE ROOT of 83 is closer to 9.
Therefore the BEST ESTIMATE would be 9.
Estimate √320
3
We know 320 is not a “perfect cube.” This means that no whole number
can be multiplied by itself three times to get 320. The closest perfect
cube less than 320 is 216. The closest perfect cube greater than 320
is 343.
√216= 6 (6x6x6=216)
3
√343 = 7 (7x7x7=343) ……… so the √320 is
3
3
between 6 and 7. Since 320 is closer to 343 than 216 the CUBE ROOT
of 320 is closer to 7. Therefore the BEST ESTIMATE would be 7.
Comparing Real Numbers (Lesson 10)
We know what a rational number is (any number that can be written as
a fraction). They include Whole Numbers, Integers, and Natural
Numbers. An irrational number is a number that is NOT rational- it
cannot be written as a fraction
REAL NUMBERS are the sets of rational and irrational numbers
combined.
Examples:
Name all the sets of numbers (types of numbers) each REAL NUMBER
belongs to:
0.25252525… = Rational Number because it is a repeating decimal but
can be rewritten as the fraction
25
99
.
√36… = Natural Number, Whole Number, Integer, AND Rational
Number because √36 = 6.
-√7… = -2.645751311…..Irrational Number because it does not end or
repeat.
Comparing and Ordering Real Numbers
**BEFORE you can compare or order you must make them the SAME
TYPE of numbers. Write numbers in decimal form in order to compare
or order.
Examples:
√7 ______2
2
3
√7 = 2.645751311…
2
2 = 2.66666666666…
3
2
Since 2.645 is less than 2.6666 √7 &lt; 2
3
15.7% ______√0.02
15.7% = 0.157
√0.02= 0.141
Since 0.157 is greater than 0.141 15.7% &gt; √0.02
4
Order the set {√30, 6, 5 , 5.3} from least to greatest.
5
√30 = 5.48
6= 6.00
4
5 = 5.80
5
5.3 = 5.3
Since 5.3 &lt; 5.48 &lt; 5.80 &lt; 6.00 The order from least to
greatest is
4
5.3, √30, 5 5 , 6
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