Download 5.10 Radicals, Irrational Numbers, and the

5.10 RADICALS,
IRRATIONAL NUMBERS,
AND THE CLOSURE AXIOMS
RADICALS

A radical is an expression that has a root

There is no real-number answer for the square root of
a negative number because no real number squared
gives a negative answer
RATIONAL AND IRRATIONAL NUMBERS


A rational number is a number that can be
written as a ratio of two integers.
An irrational number is a real number that
cannot be written as a ratio of two integers.
SETS OF NUMBERS
Real Numbers
Rational Numbers
Integers
Whole Numbers
Natural Numbers
Irrational Numbers
TELL WHETHER EACH RADICAL REPRESENTS A
RATIONAL NUMBER, AN IRRATIONAL NUMBER,
OR NEITHER
1.
2.
3.
4.
CLOSURE

A given set of numbers is closed under an operation
if there is just one answer, and that answer is in the
given set whenever the operation is performed with
numbers that are in that set.

The braces { } mean “the set of” or “the set containing”
(number is set)(operation)(number in set)=(unique number in set)
CLOSURE AXIOMS

Closure Under Multiplication
The set of real numbers is closed under
multiplication
 If x and y are any real numbers, then xy is a unique
real number.

CLOSURE AXIOMS

Closure Under Addition
The set of real numbers is closed under addition
 If x and y are any real numbers, then x + y is a
unique real number.

TELL WHETHER EACH SET OF NUMBERS IS
CLOSED UNDER THE GIVEN OPERATION. GIVE
AN EXAMPLE.

{integers}, subtraction

{rational numbers}, addition
TELL WHETHER EACH SET OF NUMBERS IS
CLOSED UNDER THE GIVEN OPERATION. GIVE
AN EXAMPLE.

{negative numbers}, multiplication

{0, 1}, addition
TELL WHETHER EACH SET OF NUMBERS IS
CLOSED UNDER THE GIVEN OPERATION. GIVE
AN EXAMPLE.

{rational numbers}, square root

{real numbers} addition
TELL WHETHER EACH SET OF NUMBERS IS
CLOSED UNDER THE GIVEN OPERATION. GIVE
AN EXAMPLE.

{negative numbers}, subtraction

{perfect squares}, square root
HOMEWORK

P 209 #1 – 43 odd