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

Answers (1)

2021-02-09

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.

Relevant Questions

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
\(\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}\)

See answers (1)

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.

See answers (1)

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.

See answers (1)

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.

See answers (1)

asked 2021-03-07

The set of whole numbers and their opposites
\(\circ\) Positive integer
\(\circ\) Ratio
\(\circ\) Absolute value
\(\circ\) Integer

See answers (1)

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

See answers (1)

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.

See answers (1)

asked 2021-02-25

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

See answers (1)

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.

See answers (1)

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?

See answers (1)

You might be interested in

determine whether the statement is true or false. Justify your answer. When your attempt to find the limit of a rational function yields the indetermi

Find the inverse of the given one-to-one function f. f(x)=(x-4)/(2x+1)

Graph the following quadratic function. First state the vertex, Iine of symmetry, y-intercept, and xintercepts. All values should be exact. Your graph must have at least three labelled points, one of which must be the vertex. f(x)=1/4 x^2+x-3

Solve the equation: \frac{3t+5}{8}=-5

Solve the equation: \frac{2x-5}{\sqrt{x+5}}

Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. f(t)=80(3/5)^t

Find the absolute value. |3-4i|

Gary made four times as much money as Joel over the summer. combined, the two made $475. How much money did each boy earn?

Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=5+54x-2x^{3}, [0,4]

Work each problem. Round to the nearest tenth of a degree, if necessary. Venus is the hottest planet, with a surface temperature of 867∘F. What is thi

Contain linear equations with constants in denominators. Solve each equation. x/3=x/2-2

Use the Zero Product Property to solve the equation: (x+5)(x+8)=0

...