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?
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.
- √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 equation 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= (2k)^2
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
true or false does this number represent a rational number 0.20200200020000200000
Is √4 Irrational?
is this seriouly the answer for the LEAP test *feecepum*
you're not going to get ALL 50 answers -_-
I am confused to, I need to know a way that you can define the two simply amd see them immediately. I am on the same level as you confusion wise but can someone just give me an easy way to do this please???
Rational numbers are numbers that can be expressed as a fraction (where the numerator and denominator are integers), while irrational numbers cannot be expressed as a fraction.
To determine whether √2, √8, and 2√3 are rational or irrational, we need to check whether they can be expressed in the form of a fraction or not.
1. √2: This is an irrational number because it cannot be expressed as a fraction. You can approximate it as 1.41421356, but it cannot be written exactly as a fraction.
2. √8: We can simplify √8 to √(4 * 2), which then becomes 2√2. Like √2, this is also an irrational number because it cannot be expressed as a fraction.
3. 2√3: This is also an irrational number since it cannot be expressed as a fraction. It is the product of 2 and the square root of 3, and cannot be simplified further.
Therefore, √2, √8, and 2√3 are all irrational numbers.
In summary:
- √2, √8, and 2√3 are irrational numbers.
- 22/7 is a rational number.
- π (pi) is an irrational number.
If you're ever unsure whether a number is rational or irrational, try to express it as a fraction. If you can, then it's rational; if you cannot, then it's irrational.