In which set(s) of numbers would you find the number sqrt80 - irrational number - whole number - rational number - integer - real number - natural number

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asked 2021-02-01

Given each set of numbers, list the
a) natural Numbers
b) whole numbers
c) integers
d) rational numbers
e) irrational numbers
f) real numbers
\(\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}\)

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asked 2021-01-23

The rational numbers are dense in \(\displaystyle\mathbb{R}\). This means that between any two real numbers a and b with a < b, there exists a rational number q such that a < q < b. Using this fact, establish that the irrational numbers are dense in \(\displaystyle\mathbb{R}\) as well.

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asked 2020-12-24

True or False?
1) Let x and y real numbers. If \(\displaystyle{x}^{{2}}-{5}{x}={y}^{{2}}-{5}{y}\) and \(\displaystyle{x}\ne{y}\), then x+y is five.
2) The real number pi can be expressed as a repeating decimal.
3) If an irrational number is divided by a nonzero integer the result is irrational.

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asked 2021-02-21

Which statement is false?
A. every irrational number is also a real number.
B. every integer is also a real number.
C. no irrational number is irrational.
D. every integer is also an irrational number.

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asked 2021-03-09

Discover prove: Combining Rational and Irrationalnumbers is \(\displaystyle{1.2}+\sqrt{{2}}\) rational or irrational? Is \(\displaystyle\frac{{1}}{{2}}\cdot\sqrt{{2}}\) rational or irrational? Experiment with sums and products of ther rational and irrational numbers. Prove the followinf.
(a) The sum of rational number r and an irrational number t is irrational.
(b) The product of a rational number r and an irrational number t is irrational.

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asked 2020-12-14

Writing and Proof: If true prove it, if false give a counterexample. Use contradiction when proving.
(a) For each positive real number x, if x is irrational, then \(\displaystyle{x}^{{2}}\) is irrational.
(b) For every pair of real numbers a nd y, if x+y is irrational, then x if irrational or y is irrational

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asked 2021-02-25

Prove that the set of irrational numbers in [0,1] is not countable

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asked 2021-01-19

\(\displaystyle{Q}:{\quad\text{if}\quad}{\left\lbrace-\frac{{3}}{{4}},\sqrt{{3}},\frac{{3}}{\sqrt{{3}}},\sqrt{{\frac{{25}}{{5}}}},{20},{1.11222},{2.5015132},\ldots,\frac{{626}}{{262}}\right\rbrace}\),
find the following
1) Rational numbers?
2) Irrational numbers?

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asked 2021-03-12

Find
a) a rational number and
b) a irrational number between the given pair.
\(\displaystyle{3}\frac{{1}}{{7}}\) and \(\displaystyle{3}\frac{{1}}{{6}}\)

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asked 2021-02-26

1) Find 100 irrational numbers between 0 and \(\displaystyle\frac{{1}}{{100}}.\)
2) Find 50 rational numbers betwee 1 and 2.
3) Find 50 irrational numbers betwee 1 and 2.

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Answer 1

Natural numbers is the set of counting numbers i.e. 1, 2, 3,…
So \(\displaystyle\sqrt{{80}}\) is not present in this set.
Whole numbers is the set of natural numbers along with 0 i.e. 0, 1, 2,…
So \(\displaystyle\sqrt{{80}}\) is not present in this set.
Integers are set of whole numbers along with negative numbers i.e. …,-2, -1, 0, 1, 2,…
So \(\displaystyle\sqrt{{80}}\) is not present in this set.
Rational numbers are set of numbers that can be expressed in the form \(\displaystyle\frac{{p}}{{q}}.\)
So \(\displaystyle\sqrt{{80}}\) is not present in this set.
Irrational numbers are set of numbers that cannot be expressed in the form \(\displaystyle\frac{{p}}{{q}}.\)
Hence \(\displaystyle\sqrt{{80}}\) is present in this set.
Real numbers are set of rational and irrational numbers together.
Hence \(\displaystyle\sqrt{{80}}\) is present in this set.
Answer: Irrational number and Real number.

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In which set(s) of numbers would you find the number sqrt80 - irrational number - whole number - rational number - integer - real number - natural number

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