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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 ? ;= - . I- - if V 2.. ~:::. "'8 ~ 1 lLJ r:T~ "/ [] 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: ,j 144. = ~ 2-) ' OYl-C- 2...\ 4[ 2- (I '\ / -1- \\CP) . (0 ( 4 .1-) ] s:-I'1\ ":.p 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 ) 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 ?~45 P=4(28) ~ 121 ::: \ \2 foo\.., - s\ ~ • ~ • So) ~ '?o D\..- = \!-?+ ~\t:>I't-\ = If2+-. .p ~ E) S-\,QU.s:. Df" poet: -:::: l }oo.f-+ +l-t-Il ~ 2.5 17.Which point best represents}[? Explain your answer. I.. AH ( I o I 1 :' 3 (' /) I I II I I • I 4 5 6 7 8 9 10 ) ~ \~ ~ 18.Which point best represents . ., IS)? Explain your answer. . /J 10 " ~~:~® 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. J144 ~ \ - 4. Co '" 5'-<. \Z5 ~~ t44 12-, !:::' j 1 J '3 -\--.:5 .. "Vis, 1.4,"...riA, ~, }[ on a number Iine. Then , order the numbers from least to greatest. ~ - < Numeric Response I. ~ ~ L.. JI<0 9 ~ ~ 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. o .. So m IS NLJM&it.$. 13£1VJ ~ ~ \£,I..!> O ~c:r ">0. U /'w'I.fiS •