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G-M > Roots and Exponent > Flashcards

Roots and Exponent Flashcards

1
Q

Square root -> never a negative number

A

sqrt(100)= 10 and never -10

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2
Q

sqrt(-16)

A

not a real number

-> we can’t find the real number with negative sqrt unlike positive

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3
Q

cuberoot(-64)

A

can be a real number (-4-4-4)

-> we can find positive number for negative cubic root

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4
Q

nsqrt(x^n)

A

|x| -> always positive

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5
Q

Square root of a whole number

A

whole number

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6
Q

Square root of non-perfect square

A

not a whole number

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7
Q

1st 11 cubic roots

A

1) 0^3= 0
2) 1^3=1
3) 2^3= 8
4) 3^3= 27
5) 4^3= 64
6) 5^3= 125
7) 6^3= 216
8) 7^3= 343
9) 8^3= 512
10) 9^3= 729
11) 10^3= 1000

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8
Q

cubicroot(-8)

A

-2-2-2= -8

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9
Q

When simplying radicals with square roots

A

simplify any perfect square and cubes

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10
Q

Approximate square roots

A

try to find the root that is inbetween and estimate it

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11
Q

cuberoot(2)

A

1.3

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12
Q

cuberoot(3)

A

1.4

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13
Q

cuberoot(4)

A

1.6

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14
Q

cuberoot(5)

A

1.7

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15
Q

cuberoot(6)

A

1.8

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16
Q

cuberoot(7)

A

1.9

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17
Q

cuberoot(8)

A

2

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18
Q

cuberoot(9)

A

2.1

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19
Q

fourthroot(2)

A

1.2

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20
Q

fourthroot(3)

A

1.3

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21
Q

fourthroot(4)

A

1.4

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22
Q

fourthroot(5)

A

1.5

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23
Q

fourthroot(6)

A

1.6

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24
Q

fourthroot(7)

A

1.6

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25
Q

fourthroot(8)

A

1.7

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26
Q

fourthroot(9)

A

1.7

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27
Q

sqrt(5)*sqrt(7) can be written as

A

sqrt(5*7)

-> to multiply them need to have same root

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28
Q

cubic(25)*cubic(5) can be expressed as

A

cubic(25*5)

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29
Q

If they don’t have the same root, can you combine them?

A

No you can’t

-> sqrt(100)*cubic(27)-> you can’t just multiply 100 and 27 n

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30
Q

Dividing radicals can be combined

A
  • > sqrt(54)/sqrt(6)= sqrt(54/6)

- > cubic(24)/cubic(3)= cubic(24/3)

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31
Q

When expression has radicals and nonradicals

A

multiply radicals with radicals and nonradicals with nonradicals
-> 2sqrt(10)4sqrt(7)= 24sqrt(10*7)

32
Q

You can add and subtract radicals that

A

are like: if they have the same root index and the same radical expression under the radical
-> 9sqrt(4)+2sqrt(4)= 11sqrt(4)

33
Q

Remove the radicals in the denominator by

A

multiplying the denomiantor by the sqrt

34
Q

Conjugate when you have radicals and non radicals being added/subtracted

A

(a-sqrt(b)) +> conjugate (a+sqrt(b))

35
Q

Square root is always

A

postive in expection of 0

36
Q

x^2

A

|x|

  • > x^2=4
  • > x=+-sqrt(4)
  • > = +-2
37
Q

even indexed root is

A

always postive

38
Q

sqrt((x+y)^2)

A

|x+y|

39
Q

when we have square root in an equation

A

isolate the square root and solve it

  • > 3sqrt(x-1)-7= 2
  • > 3sqrt(x-1)= 9
40
Q

If n is a postive integer, m^n means

A

n factors m being multiplied

  • > n^5= nnnnn -> not same as (5n)
  • > 2^4= 22222
  • > (xy)^3= (xy)(xy)(xy)
41
Q

If a^x=a^y

A

x=y

42
Q

a^x* a^y = a^z

A

x+y=z

43
Q

When multiplying like base

A

add the exponent

-> (x^a)(x^b)= x^(a+b)

44
Q

Dividing like bases

A

subtract the exponents

  • > x^a/x^b= x^(a-b)
  • > (xn)^5x/(xn)^2x
45
Q

When there are exponent that are being raised to a power

A

multiply thos exponents

  • > (x^a)^b= x^ab
  • > (x^4)^2= x^8
46
Q

If the bases are not same

A

try to make the bases same and add them

47
Q

Mulitplication of different bases and like expoent

A

multiply the base

  • > (2^4)(3^4)= 6^4
  • > (x^a)(y^a)= (xy)^a
48
Q

Division of different bases and like exponent

A

keep the common exponent and divide th bases

  • > x^a/y^a= (x/y)^a
  • > (12^4)/(3^4)= (12/3)^4
49
Q

When non-prime factorization raised to the power

A

can be reduced through prime factorization

-> 6^80= (3*2)^80

50
Q

Can simplify the fractions and multiplication with

A

prime factorization

51
Q

radicals can be expressed as exponents

A

sqrt(x)= x^1/2

52
Q

Exponents notation can be factored

A

-> you can factor the GCF out

x(x^9)

53
Q

Raising a base to a negative exponent by

A

take the reciprocal of the base and exponent while turning the negative exponent into a postive exponent

  • > 2^-2= 1/(2^2)
  • > 10^-4 = 1/10^-4
  • > x^-y= 1/x^y
54
Q

(x/y)^-z

A

(y/x)^z

55
Q

non zero base raise to 0 equals (x^0)

A

1

56
Q

base raise to the value of the expression (5^1)

A

is simply the base

-> 5^1= 5

57
Q

2^n+2^n=

A

2^n+1

58
Q

when we need to add or subtract

A

use LCM like you sue it for others

59
Q

If we need to compare the fractions and have exponent in the denominator

A

you can find LCM

60
Q

Base is less than -1 and exponent is an even positive integer

A
  • result is larger

- > (-4)^2= 16

61
Q

Base is less than -1 and exponent is an odd positive integer

A
    • result is smaller

- > (-4)^3= 64

62
Q

Base is positive proper fraction and exponent is even positive integer

A
  • > Result is smaller

- > (1/4)^2= 1/16

63
Q

Base is negative proper fraction and exponent is even positive integer

A

(-1/4)^2= 1/16

64
Q

Base is positive proper fraction and exponent is odd positive integer

A
  • > result is smaller

- > (1/4)^3= 1/64

65
Q

Base is negative proper fraction and exponent is odd positive integer

A
  • > result is larger

- > (-1/4)^3= -1/64

66
Q

0

A

x^2

67
Q

Two number with same base and exponent can differ

A

by as little as 1

  • > 9^7= 4,782,969
  • > 9^8= 43,046,721
68
Q

power of ten raised to exponent

A

just add a 0
to the 1
-> 10^1= 10
-> 10^2= 100

69
Q

can be written in scientific notation

-> 6*10^-6

A

= 6,000,000

-> to convert into scientific notation, coefficient must be between 1 and 10

70
Q

Converting to the scientific notation: n is greater than 10

A

move the decimal point enough to the left until it becomes a number between 1 and 10
-> 9.3*10^7= 93,000,000

71
Q

If n is between 0 and 1

A

Move the decimal point enough places to the right until it becomes a number between 1 and 10
-> 0.0000678= 6.78*10^-5

72
Q

When multiplying or dividing number in scientific notation or number almost in scientific notation

A

the coefficient can be multiplies or divided separately from the power of ten

73
Q

When a perfect square root ends with an even number of zeros

A

square roots of such a perfect square will have exactly half the number of zeroes to the right of the final nonzero digit as a perfect square

  • > sqrt(10,000)= 100
  • > sqrt(81,000,000)= 9000
74
Q

If a decimal with a finite number of decimal places is a perfect square, its square root will have

A

exactly half the number of decimals places

-> thus a perfect square decimal must have an even number of decimals

75
Q

The cube root of a perfect cube integer has

A

exactly one third the number of zeroes

-> cuberoot(1,000)= 10

76
Q

Squaring decimal with zeroes

i.e (0.000005)^2 -> we have 6 decimals

A

-> 2*6= 12
-> as 5^2 has 2 decimals we add 10 zeroes
-> (0.000005)^2
= 0.000000000025

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