Posted by Sanchia on Monday, June 15, 2009 at 11:10pm.
what are rational and irrational numbers??
i know that irrational numbers are numbers that cannot be expressed as a fraction, but i'm still confused.
there is this question:
which of the following are irrational numbers: √2, √8, 22/7, pi, 2√3
i know that 22/7 is rational, pi is irrational, but what about those square roots?
- irrational numbers?! - drwls, Monday, June 15, 2009 at 11:49pm
Square roots of numbers that are not the squares of integers are all irrational. There is a way to prove that but I forgot the details. You have to assume that a fraction works and then prove that the assumption leads to a contradiction
Any number that does not meet the definition of being rational is irrational.
- irrational numbers?! - Reiny, Tuesday, June 16, 2009 at 12:55am
- √2 is either rational or irrational.
- Assume that √ is rational so that
√2 = a/b, with a/b in lowest terms
- Square both sides to get
2 = a^2/b^2
then a^2 = 2b^2
- the right side of this eqation is clearly an even number, since anything multiplied by 2 is even
- so a^2 must be even. We also know that if we square an odd number the result is odd, and if we square an even number the result is even
so a must be even
so a could be written as 2k
- rewriting our equation as
2b^2 = 4k^2
b^2 = 2k^2
by the same argument as above 2k^2 is even , so b has to be even
which means a and b are both even, therefore a/b is not in lowest terms
BUT that contradicts my assumption that a/b was a fraction in lowest terms
so √2 = a/b is a false statement
therefore √2 cannot be rational, and
must then be irrational
the same argument could be used for √3 and all other square roots
- irrational numbers?! - brandy, Tuesday, September 1, 2009 at 4:55pm
true or false does this number represent a rational number 0.20200200020000200000
- irrational numbers?! - Amber, Thursday, April 21, 2011 at 5:15pm
Is √4 Irrational?
Answer this Question
- math - Which statement is true? A. All irrational numbers are also rational ...
- Math - What are irrational, rational, and natural numbers? A rational number is ...
- Algebra - 28. Use the Distributive Property to simplify x(4x^2 + x + 4) Is it 4x...
- math - 1. Which of the following numbers is an example of an integer? a. -15 b. ...
- 9th grade - Name the set(s) of numbers to which 1.68 belongs. a. rational ...
- math - hi i need help with rational and irrational numbers. i just need to know ...
- Math - Are there more rational or irrational numbers? I am thinking irrational, ...
- Math Logic - If there are as many rational numbers as there are irrational ...
- Algerba II - Hi Do decimals such as 2.718 represent rational numbers or ...
- math - What is the best sequence of names to identify this set of numbers? (1 3/...