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)

## 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)

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# 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