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SECONDARY
ALGEBRA
ALGEBRA I
IRRATIONAL NUMBERS
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Irrational numbers problems solved
Recent questions in Irrational numbers
Irrational numbers
asked 2021-03-12
Find
a) a rational number and
b) a irrational number between the given pair.
\(\displaystyle{3}\frac{{1}}{{7}}\)
and
\(\displaystyle{3}\frac{{1}}{{6}}\)
Irrational numbers
asked 2021-03-09
Cindy separated her fruit flies into equal groups. She estimates that there are 2¹⁰ fruit flies in each of 2² jars. How many fruit flies does Cindy have in all?
Irrational numbers
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.
Irrational numbers
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.
Irrational numbers
asked 2021-02-25
Prove that the set of irrational numbers in [0,1] is not countable
Irrational numbers
asked 2021-02-21
Find the value of the following expression:
\(\displaystyle{4}\sqrt{{2}}+{2}{\left(\sqrt{{36}}-\sqrt{{8}}\right)}\)
Irrational numbers
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.
Irrational numbers
asked 2021-02-20
Integers that are not whole numbers
Irrational numbers
asked 2021-02-19
Simplify the following:
(a+10)(a+10)
Irrational numbers
asked 2021-02-13
Determine whether the below given statement is true or false. If the statement is false, make the necessary changes to produce a true statement:
All irrational numbers satisfy |x - 4| > 0.
Irrational numbers
asked 2021-02-11
Consider the following statements. Select all that are always true.
The sum of a rational number and a rational number is rational.
The sum of a rational number and an irrational number is irrational.
The sum of an irrational number and an irrational number is irrational.
The product of a rational number and a rational number is rational.
The product of a rational number and an irrational number is irrational.
The product of an irrational number and an irrational number is irrational.
Irrational numbers
asked 2021-02-08
In which set(s) of numbers would you find the number
\(\displaystyle\sqrt{{80}}\)
- irrational number
- whole number
- rational number
- integer
- real number
- natural number
Irrational numbers
asked 2021-02-02
Cindy separated her fruit flies into equal groups. She estimates that there are 2¹⁰ fruit flies in each of 2² jars. How many fruit flies does Cindy have in all?
Irrational numbers
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
\(\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}\)
Irrational numbers
asked 2021-01-31
4sqrt8xxsqrt10=?ZSKPSK
Irrational numbers
asked 2021-01-28
Find the outcome of:
\(\displaystyle{\cos{{\left(\frac{\pi}{{4}}+\frac{\pi}{{3}}\right)}}}\)
Irrational numbers
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.
Irrational numbers
asked 2021-01-19
\(\displaystyle\sqrt{{96}}=\sqrt{{4}}\times\sqrt{{48}}\)
\(\displaystyle={2}\times\sqrt{{48}}\)
\(\displaystyle={2}\times\sqrt{{8}}\times\sqrt{{6}}\)
\(\displaystyle={2}\times{4}\times\sqrt{{6}}\)
\(\displaystyle={8}\sqrt{{6}}\)
Is there a mistake in the simplification? What is it? Correct the mistake if there is one and simplify sqrt96.
Irrational numbers
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?
Irrational numbers
asked 2021-01-13
Simplify the following expression:
\(\displaystyle\frac{{8}}{{{4}-\sqrt{{{6}{n}}}}}\)
1
2
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