Download Roots Quiz Study Guide Scheduled for: February 16, 2017

Roots Quiz Study Guide
Scheduled for: February 16, 2017
Roots (Lesson 8)
You are expected to know the perfects squares up to 20!
Examples:
√64 = 8 (Since 8 x 8 = 64)
Ex. 2:
− √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
Ex. 3:
±√1.21 = ± 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
"plus or minus."
±√1.21 = ± 1.1
Ex. 4:
T​2 ​= 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 = ±13
T= ±13
Ex. 5: √− 16
*You CANNOT find the square root of a negative number!*
There is ​no real solution​.
Cube Roots
You should know the perfect cubes up to 10!
Example​: √3 729 ​ = 9
​(9 x 9 x 9= 729)
Example: √− 729 = -9
(-9 x -9 x -9= 729)
*You CAN take the cube root of a negative number!*
3
Example: x​3 ​= 27 ​(to cancel something being cubed we need to find the cube root)
3
3
√x3 = √27
x=3
Estimating with Roots (Lesson 9)
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.
Estimating to the nearest tenth​!
√83 is very close to the √81 ​which equals 9. Therefor we know the √83 ​is in
the low 9’s.
Guess and check on calculator: 9.1 x 9.1 = 82.81
9.2 x 9.2 = 84.64
√83 ≈ 9.1
(very close to 83)
3
Estimate √320
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.
√3 216 = 6 (6x6x6=216)
√3 343 = 7 (7x7x7=343) ……… so the √3 320 is
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)
Comparing and Ordering Real Numbers
**BEFORE you can compare or order you must make them the SAME
TYPE of numbers. Write numbers in d
​ ecimal form​ in order to compare
or order.
√7 ______2 23
√7 = 2.645751311…
2 23 ​= 2.66666666666…
Since 2.645 is less than 2.6666 √7 <2 23
Example:
15.7% ______ √0.02
15.7% ​= 0.157
√0.02 = 0.141
Since 0.157 is greater than 0.141 1
​ 5.7% > √0.02
Ordering Real Numbers:
Order the set { √30 ​,6, 5 45 , 5.3​} from least to greatest.
√30 ​= 5.48
6​= 6.00
5 45 ​ = 5.80
5.3​ = 5.3
Since 5.3 < 5.48 < 5.80 < 6.00 The order from least to greatest is
5.3,
√30 ​, ​5 45 ​, 6