8th Grade Math - Roots & Real Numbers
True or False? All fractions are irrational.
False Fractions cannot be made out of irrational numbers
True or False? Repeating decimals are irrational?
False Irrational numbers cannot be terminating or repeating
True or False? Natural numbers include zero.
False Natural numbers are 1, 2, 3, 4....---->
True or False? All negative number are integers.
False Only whole numbers and their opposites are integers. For example -1.6 is not an integer but -1 is an integer.
True or False? Whole numbers can be negative.
False Whole numbers are 0, 1, 2, 3.... ----->
What is R ?
Real Numbers Everything! (except imaginary which you haven't learned about)
Definition: To square a number?
The number we get after multiplying and integer by itself
Definition: The square root of a number?
The value that when multiplied by itself gives the number
True or False: √ab = √a*√b
True
True or False? ³√-a = -³√a
True (See Lesson 3.2)
True or False? ³√ab = ³√a * √b
True (See Lesson 3.2)
True or False? All integers are rational numbers.
True Because fractions can't be made out of irrational numbers
True or False? Irrational numbers are real.
True Rational numbers & irrational numbers are real
True or False? Terminating decimals have an end and are real.
True Terminating means end and it is true that terminal & repeating decimals are rational
What is a "non-real" number?
A number that is not: a natural number or a whole number or an integer or a rational number or an irrational number Imaginary numbers are non-real
True or False? Irrational numbers can be fractions.
False Fractions and decimals are rational numbers
What is the difference between: 1) Radical 2) Radicand 3) Index
1) √ 2) √x the x is the radicand 3) √x the idex is 2 (whenever there is no index assume it is 2)
How do we estimate where imperfect squares fall on a number line? Example: √ √75 √ Between _____ and _____ but closer to _____
Bracketing 1) √64 √75 √81 √64 = 8 √75 √81 = 9 so √75 is between 8 and 9 but closer to 9 (because 75 is closer to 81 than 64)
What is Z ?
Integers -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5........---> (Includes Zero!) (Includes Negatives of all Whole Numbers!) (Not Fractions or Decimals!)
What is Q' ?
Irrational Numbers Examples are π, 3.14159 which is pi, √2, √3, e, X/0, Non-termination
What is N ?
Natural Numbers 1, 2, 3, 4, 5, 6, 7........---> (Not Zero!)
What is the square root of √-1 ? What is the square root of √-25? What is the square root of √-49?
No Solution Can NEVER have a square root of a negative number Example: -1*-1=1 and 1*1=1 so you can never take a number multiplied by itself and get a negative number
What is Q ?
Rational Numbers Includes All Natural, Whole, Integers AND Fractions & all Terminating or Repeating Decimals
What is W ?
Whole Numbers 0, 1, 2, 3, 4, 5, 6, 7........---> (Includes Zero!)
What is? a) √121 b) √144 c) √169 d) √196 e) √225 f) √256 g) √289 h) √324 i) √361 j) √400
a) 11 b) 12 c) 13 d) 14 e) 15 f) 16 g) 17 h) 18 i) 19 j) 20
What is? a) √4 b) √9 c) √16 d) √25 e) √36 f) √49 g) √64 h) √81 i) √100
a) 2 b) 3 c) 4 d) 5 e) 6 f) 7 g) 8 h) 9 i) 10
Which is the index in the expression ³√125 ? a) 3 b) 5 c) 125 d) √
a) 3
Find the cube root of 64 a) 4 b) 8 c) 16 d) 32
a) 4 Because 4 * 4* 4 = 64
Between which two values is ³√200 ? (Between which two values is cube root of 200?) a) 5 and 6 b) ³√5 and ³√6 c) 199 and 201 d) 10 and 20
a) 5 and 6 ₃√125 = 5 ₃√200 so it is between 5 and 6 ³√216 = 6
What is √25 a) In words? b) Expanded form? c) Value?
a) Square root of 25 b) √5*√5 c) 25
Is √13 closer to 3 or 4? a) 3 b) 4
b) 4 Because 3*3=9 and 4*4=16 so 13 is closer to 4 than 3.
Which is NOT a perfect square? a) 49 b) 50 c) 64 d) 100
b) 50 Because √50 = 5√2
Which is the radicand in the expression ³√125 ? a) 3 b) 5 c) 125 d) √
c) 125
Between which two values is √75 ? a) 64 and 81 b) √8 and √9 c) 8 and 9 d) 74 and 76
c) 8 and 9 √64 = 8 √75 so it is between 8 and 9 √81 = 9
Which answer is an example of a expression that has no real root or no solution in the real number? a) Cube root of -8 b) -√25 c) √-25
c) √-25 Can NEVER have a NEGATIVE radicand inside a SQUARE radical
Which is an algebraic representation of the "square root of 64"? a) 64² b) 8² c) √64
c) √64
Find √100 a) 10,000 b) 50 c) 20 d) 10
d) 10
The "square of a number" is shown algebraically by which expression? a) 2x b) x+2 c) √x d) x²
d) x² Notice it said "the square of a number" not the "square ROOT of a number"
Which is the radica3 in the expression ³√125 ? a) 3 b) 5 c) 125 d) √
d) √
What is: (25)½
√25