Square & Cube roots, Rational numbers
Law for power of a quotient
(a/b)^n = a^n/b^n, b is not equal to 0
Examples of Rational Numbers
-Whole numbers -decimals -Integers -perfect squares or cubes -fractions -percents
Examples of Irrational Numbers
-imperfect squares -Pi -quare root of 3,5, and 7
3/5 • 5/3 = ?
1
cubed 1
1
Cube root of 1?
1 because 1*1*1=1
Cube root of 10?
1,000 because 10*10*10=1,000
cubed 1,000
10
Cube root of 5?
125 because 5*5*5=125
Square root of 4
2
cubed 8
2
3.28 • 0.88
2.8864
Cube root of 6?
216 because 6*6*=216
Cube root of 3?
27 because 3*3*3=27
Square root of 9
3
cubed 27
3
What is 3 cubed?
3*3*3= 27
What is 3.28 ÷ 0.88?
3.727272727272727
Cube root of 7?
343 because 7*7*7=343
3√64
4
Cube root of 64?
4
Square root of 16
4
cubed 64
4
4 Cubed
4*4*4= 64
Cube root of 125?
5
Square root of 25
5
cubed 125
5
5 Cubed
5*5*5= 125
Cube root of 8?
512 because 8*8*8=512
Cube root of 216?
6
Square root of 36
6
cubed 216
6
√36
6
Cube root of 4?
64 because 4*4*4=64
Square root of 49
7
cubed 343
7
Cube root of 9?
729 because 9*9*9=729
cubed 512
8
Cube root of 2?
8 because 2*2*2=8
cubed 729
9
Rational Number
A number than can be expressed in the form a/b where b ≠ to 0.
Perfect Square
A number that can be expressed as the product of two equal integers.
Square Root
A number that when multiplied by itself equals a given number.
Cube Root
A special value the when cubed gives the original number.
BEDMAS
Brackets Exponents Division Multiplication Addition Subtraction
Irrational Numbers
Never ends, 3.14...., .71711..., etc.
Whole Numbers
No decimals or fractions, Natural numbers including 0.
Irrational Number
Number that can't be expressed in the form where a and b are integers and b ≠ to 0.
Square Root
Product/Number multiplied by itself.
Real Numbers
Rational and Irrational
36 6 ___ = ___ 49 7
Square root of 36 is 6, and the square root of 49 is 7. This is just in fraction form.
Rational Numbers
Stops, for example 10.2, or 1.121231234..., .2323, etc.
Radicand
The expression under a radical sign.
All Real Numbers
The numbers used to count.
To find the square root, ask yourself _____?
What number times itself gives me the product?
multiplicitive inverse
When you multiply a number by its reciprocal and it is equal to 1.
Integers
Whole numbers and their opposites.
Perfect Squares:
Whole numbers multiplied by itself.
Perfect square
a number that has a whole number as its square root 81 → 9 x 9 - 81 9 is a whole number
Law for power of a product
the power is multiplied to each (ab)^m = a^mb^m
Law for multiplying powers
the powers are added (a^m)(a^n) = a^m+n
Law for power of a power
the powers are multiplied (a^m)^n = a^mn
Law for dividing powers
the powers are subtracted a^m ÷ a^n = a^m-n
Square root
the square root of a given number is the value that when multiplied to itself results in the number s.r. of 9 is 3 → 3 x 3 = 9
Estimating square roots
use the perfect square above and below the given number 104 → 100 is the nearest smaller perfect square 121 is the nearest larger perfect square √100 = 10 and √121 = 11 21 numbers between 100 and 121, so 104, is 4/21 = 0.2 √104 is approx. 10.2
√2000
≈45