Irrational Numbers: Examples & Non-Examples Explained

High School
Algebra
Algebra I
Irrational numbers

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.

Rui Baldwin 2021-02-11

Consider the following statements.
a)The sum of a rational number and a rational number is rational.
b)The sum of a rational number and an irrational number is irrational.
c)The sum of an irrational number and an irrational number is irrational.
d)The product of a rational number and a rational number is rational.
e)The product of a rational number and an irrational number is irrational.
f)The product of an irrational number and an irrational number is irrational.

foass77W 2021-02-08

In which set(s) of numbers would you find the number $\sqrt{80}$
- irrational number
- whole number
- rational number
- integer
- real number
- natural number

ediculeN 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?

Dolly Robinson 2021-02-01

For each set of numbers, list the
a) natural Numbers
b) whole numbers
c) integers
d) rational numbers
e) irrational numbers
f) real numbers
${- 6, \sqrt{23}, 21, 5.62, 0.4, 3 \frac{2}{9}, 0, - \frac{7}{8}, 2.074816 \dots}$

Jason Farmer 2021-01-31

To find the equation $4 \sqrt{8} \times \sqrt{10} = ?$

geduiwelh 2021-01-28

Find the outcome of:
$\cos (\frac{π}{4} + \frac{π}{3})$

BenoguigoliB 2021-01-23

The rational numbers are dense in $R$ . 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 $R$ as well.

postillan4 2021-01-19

$Q : if {- \frac{3}{4}, \sqrt{3}, \frac{3}{\sqrt{3}}, \sqrt{\frac{25}{5}}, 20, 1.11222, 2.5015132, \dots, \frac{626}{262}}$ ,
find the following
1) Rational numbers?
2) Irrational numbers?

beljuA 2021-01-13

Simplify the following expression:
$\frac{8}{4 - \sqrt{6 n}}$

Cabiolab 2021-01-10

Find the value of the following expression:
$\frac{\sin (x)}{\cos (- x)} + \frac{\sin (- x)}{\cos (x)}$

avissidep 2021-01-06

Write two rational and three irrational numbers that are between 3 and 4 with explanation.

Wierzycaz 2020-12-24

True or False?
1) Let x and y real numbers. If $x^{2} - 5 x = y^{2} - 5 y$ and $x \neq y$ , 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.

Chesley 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 $x^{2}$ 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

Tahmid Knox 2020-12-03

Write each number in standard form. $(2 \cdot 1) + (6 \cdot (\frac{1}{1000}))$

Nannie Mack 2020-11-23

The sum of the number and its squareroot is 90. What is the number?

Jerold 2020-11-22

How to find a rational number halfway between any two rational numbers given infraction form , add the two numbers together and divide their sum by 2. Find a rational number halfway between the two fractions in each pair.
$\frac{1}{4}$ and $\frac{3}{4}$

Bergen 2020-11-09

Find $\sqrt[4]{25^{2}}$

Khaleesi Herbert 2020-10-27

What is $\sqrt{7 \sqrt{7 \sqrt{7}}}$ ?

chillywilly12a 2020-10-20

What is the square root of -98?

The use of irrational numbers is quite common for the Engineering disciplines where various irrational numbers equations are used to determine the rightfulness of some calculations or tasks that require prognosis. As a way to make things easier, you can take a look at the list of questions related to irrational numbers and receive immediate help as you look through the list of answers.

If you need additional assistance or feel unsure about your task, simply compare these examples with your task and proceed from there.

Algebra I

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