# Algebra 1

Name The Subsets Of The Real Numbers To Which Each Number Belongs:
A.-2.324
B.Square Root Of 46

I don't even know what this stuff means. Please help!

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1. A) Real/Rational
B) Real/Irrational

because -2.324 = (-2324/1000)
but sqrt(46) cannot be expressed as a fraction

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2. There are various classes of numbers. In order of increasing "size" we have

whole numbers: 1,2,3,4,...
integers: ...-3,-2,-1,0,1,2,3,...
rational numbers (fractions): 1/2, 3/7, 98/113, etc
Rational numbers include also
terminating decimals: 2.5, 123.456, 99.32764, etc.
repeating decimals: 1.22222..., 9831279.2397239239239...

irrational numbers: everything else. They are decimal numbers which go on forever without repeating. Such as

√7 = 2.64575...
π = 3.14159265...
and so on

roots may be rational or even integers, if the radicand is a perfect power:

√36 = 6 because 6^2 = 36
√2.25 = 1.5 because 1.5^2 = 2.25
∛27 = 3 because 3^3 = 27
and so forth

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