2√ 4√ 20−−√ 25−−√ Explain a strategy for classifying each radical as rational or irrational.
Answers
Answer:
Whole numbers
\greenD{\text{Whole numbers}}Whole numbersstart color #1fab54, start text, W, h, o, l, e, space, n, u, m, b, e, r, s, end text, end color #1fab54 are numbers that do not need to be represented with a fraction or decimal. Also, whole numbers cannot be negative. In other words, whole numbers are the counting numbers and zero.
Examples of whole numbers:
4, 952, 0, 734,952,0,734, comma, 952, comma, 0, comma, 73
Integers
\blueD{\text{Integers}}Integersstart color #11accd, start text, I, n, t, e, g, e, r, s, end text, end color #11accd are whole numbers and their opposites. Therefore, integers can be negative.
Examples of integers:
12, 0, -9, -81012,0,−9,−81012, comma, 0, comma, minus, 9, comma, minus, 810
Rational numbers
\purpleD{\text{Rational numbers}}Rational numbersstart color #7854ab, start text, R, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end text, end color #7854ab are numbers that can be expressed as a fraction of two integers.
Examples of rational numbers:
44, 0.\overline{12}, -\dfrac{18}5,\sqrt{36}44,0.
12
,−
5
18
,
36
44, comma, 0, point, start overline, 12, end overline, comma, minus, start fraction, 18, divided by, 5, end fraction, comma, square root of, 36, end square root
Irrational numbers
\maroonD{\text{Irrational numbers}}Irrational numbersstart color #ca337c, start text, I, r, r, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end text, end color #ca337c are numbers that cannot be expressed as a fraction of two integers.
Examples of irrational numbers:
-4\pi, \sqrt{3}−4π,
3