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Expressions and the Number System STUDY GUIDE: Exponents, Roots, Irrational and Rational Numbers. Complete the following problems in your Spiral Notebooks: Show Work, easier to study from!! I. S~mplify:
~
1
6"6 . ;=
(g
-Lot to .l.o. '-n' ~ . LP' to -Co' to -=~
2. Simplify:
H)-'xH)'~
CAC:::n0
&Z")
~~
3. Simplify USing exponents:
4. Simplify the expression:
\
)2
6'
v
=
'-'
xi
.A
-,A/_
/fYV-V· V-V
5. What is equivalent to
6. S.il~plifY:
M.
7.
-
-;:;
3
r
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;=
-
.
I-
- if
V
2.. ~:::. "'8
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1
lLJ
r:T~
"/
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2
8. Evaluate 2w- zO fonv'
= 10 and z = 2. -::::)
-'l...) (V\
2. ( \ 0
2. J:=
9. A student has 4 cubes and each cube measures 4 units on
represents the combined surface area of all 4 cubes
10. Find:
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4[
2- (I '\ /
-1- \\CP)
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(0 ( 4 .1-) ]
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II. Simplify:
,,/25 + ,)36.
:::
5 +-eo
~
-:::'\~
12. Simplify: 2JI6 +40 . -== 2.(4)+4D -= ~ ~ -r40
13. Find all square roots of the number 225.
14. Evaluate:
.
,f81 - ' -Jr:;;_
~). - 9 - 5
Q
15. What is equivalent to:
L\5
@
=4
A+re;. ­
15]
~
l.±!J
I '\ ~ L
'-T J -
I
- _
100 - 51
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16. Randal's dad is installing a new pool in their backyard. The pool is a square and has an area of 121 ft-.
Randal's dad will then build a 7 ft wide deck to surround the pool. What is the outside perimeter of the deck?
deck
A
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P=4(28)
~ 121 ::: \ \2­
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poet: -:::: l
}oo.f-+
+l-t-Il ~ 2.5
17.Which point best represents}[? Explain your answer.
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1
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3
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II
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4
5
6
7
8
9
10
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18.Which point best represents . ., IS)? Explain your answer.
.
/J
10
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J9.Which of these expressions is true?
.J36 < 5 or 53 < 122
20 .Betweeo whet two ;otegm does
21. Estimate
)
.Jl56 I;e'
- .,/21 to the nearest tenth.
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5'-<.
\Z5
~~
t44
12-, !:::'
j
1
J '3 -\--.:5
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"Vis, 1.4,"...riA, ~, }[ on a number Iine. Then , order the numbers from least to greatest.
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Numeric Response
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22.Which whole number is the best approximation for "./(.-.) 3)2 + 5? Explain.
23 .Graph the numbers
~
t:t-
o
2
Find the value of',/5 + 122.
),4
{f
%Y
'TI
.,e 7
==
JZ 5-+[4-4
Essay
I. Explain why the exponents in each of the following expressions cannot be added.
301 + 3°
'I r.
~~
1\Jc91
~ 'GK.fh1'J~..s
'-' • -) <E-- CAN N O~ rtvP C-~D ~~
2 . Plot
w \-\-t-,...)
~- ,1'
wH'O-J
ffisbl ~~ ~ t--.)JM~.
HLlL1\Pt.>..-jI~~ 1)1~
~
, /71 on a number line. Explain how you know the location is correct.
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