# To check: Whether the set of numbers {sqrt{3}, pi, frac{sqrt[3]{2}}{4}, sqrt{5}} contains integers, rational numbers, and (or) irrational numbers.

Question
Decimals
To check: Whether the set of numbers $$\displaystyle{\left\lbrace\sqrt{{{3}}},\pi,{\frac{{\sqrt{{{3}}}{\left\lbrace{2}\right\rbrace}}}{{{4}}}},\sqrt{{{5}}}\right\rbrace}$$ contains integers, rational numbers, and (or) irrational numbers.

2020-10-19

Result used: Rational number: Rational numbers are numbers that can be written in the form $$\displaystyle{\frac{{{p}}}{{{q}}}}$$, where p and q are integers with $$\displaystyle{q}\ne{q}{0}$$. The rational numbers can be written as terminating or repeating decimals. Irrational number: The irrational numbers are set of all real numbers that not rational numbers. The irrationals cannot be written as terminating or repeating decimals. Verification: The given set of numbers is $$\displaystyle{\left\lbrace\sqrt{{{3}}},\pi,{\frac{{\sqrt{{{3}}}{\left\lbrace{2}\right\rbrace}}}{{{4}}}},\sqrt{{{5}}}\right\rbrace}$$ Observe that the elements $$\sqrt{3}=1.732\cdots,\pi=3.14\cdots,\frac{\sqrt{3}\{2\}}{4}=0.315\cdots,\text{and}\sqrt{5}=2.236\cdots$$ are non-terminating decimals. Therefore, by the definition of the irrational numbers, all the numbers in the given set are irrational. Answer: Thus, the set numbers $$\displaystyle{\left\lbrace\sqrt{{{3}}},\pi,{\frac{{\sqrt{{{3}}}{\left\lbrace{2}\right\rbrace}}}{{{4}}}},\sqrt{{{5}}}\right\rbrace}$$ contains irrational numbers.

### Relevant Questions

How do you know by inspection that the solution set of the inequality $$x+3>x+2$$ is the entire set of real numbers?
Express irrational solutions in exact form and as a decimal rounded to three decimal places.
$$\log_{2}(3x+2)-\log_{4}x=3$$
Which of the following numbers are NOT integers?
$$2,\ -0.5,\ -5,\ 1/2,\ 0$$
Given each set of numbers, list the
a) natural Numbers
b) whole numbers
c) integers
d) rational numbers
e) irrational numbers
f) real numbers
$$\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}$$
To solve for 'n', we need to cross multiply
Given equation :
$$\frac{3}{n}=\frac{5}{16}$$
For digits before decimals point, multiply each digit with the positive powers of ten where power is equal to the position of digit counted from left to right starting from 0.
For digits after decimals point, multiply each digit with the negative powers of ten where power is equal to the position of digit counted from right to left starting from 1.
1) $$10^{0}=1$$
2) $$10^{1}=10$$
3) $$10^{2}=100$$
4) $$10^{3}=1000$$
5) $$10^{4}=10000$$
And so on...
6) $$10^{-1}=0.1$$
7) $$10^{-2}=0.01$$
8) $$10^{-3}=0.001$$
9) $$10^{-4}=0.0001$$
$$\sum_{n=1}^\infty \frac{(-1)^n}{(2n)!}$$
a) $$(2,-2)$$
b) $$(-1,\sqrt{3})$$
Find the polar coordinates $$(r,\theta)$$ of the point, where r is greater than 0 and 0 is less than or equal to $$\theta$$, which is less than $$2\pi$$
Find the polar coordinates $$(r,\theta)$$ of the point, where r is less than 0 and 0 is less than or equal to $$\theta$$, which is less than $$2\pi$$