Exponent & Square Root  – Basic College Mathematics for Teachers

Reference:  K. Elayn Martin-Gay – Page 1       Definition:  Exp & SqRt

 

Exponents

A special & repeated multiplication

of Base Number dictated from Exponent.

 

40 =  1      41 = 4      42 = 16      43 = 64

 

42 =  4 x 4 = 16        72 =  7 x 7 = 49

 

Base Exponent  =  Number

Square Roots

A special & duplicate division

 ( √ means Square Root )

 

√1      √4      √9      √16    √25

√36    √49    √64    √81    √100

 

√16 = 4   since   4 x 4 = 16

√49 = 7   since   7 x 7 = 49

Interpolation of Exponents

 

41 = 4       4X = 8     42 = 16

 

Since the number 8 is between 4 & 16,

logically assume X is between 1 & 2.

Therefore:  4    8    16

Between 4&8=4   Between 8&16=8

Therefore:  X= 1 4/8 (Approximately)

Check Estimations with Calculator!

Interpolation of Square Roots

 

√9 = 3        √13 = X        √16 = 4

 

Since the number 13 is between 9 & 16,

logically assume X is between 3 & 4.

Therefore:  9    13    25

Between 9&13=4   Between 9&16=7

Therefore:  X = 3  4/7  (Approximately)

Check Estimations with Calculator!

 

Counting and Natural Numbers

 

Counting Numbers:   1,2,3,4,5,   etc…

 

Natural Numbers:   1,2,3,4,5,  etc…

 

Single or Double or Triple Digit Numbers?

Can you think of any other type of numbers?

 

 

Even and Odd Numbers

 

Even Numbers:    2,4,6,8, etc…

 

Odd Numbers:   1,3,5,7,  etc…

 

Do Even & Odd have any numbers in common?

Do Even and Odd have anything in common?

Rational Numbers

 

Any Number whose Decimal Equivalent

Stops   or   Does Not Repeat.

 

4/5 = .8        3/4 = .75      5/8 = .625

 

1 1 2 = 1.5              3  1/5 = 3.2

Irrational Numbers

 

Any Number whose Decimal Equivalent

Does Not Stop or Does Not Repeat.

 

2/3 = .666…         5/6 = .8333…

 

…  means the number repeats.

Thomas Love             Malone College              2006/2008