Rational or not?
3 + 1 2 − 2 7 Is the number above rational or irrational?
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6 solutions
Nice problem and solution! (+1)
3 + 1 2 − 2 7
= 3 + 2 3 − 3 3
= 3 3 − 3 3
= 0
Relevant wiki: Surds
3 + 1 2 − 2 7 .
= 3 ( 1 + 4 − 9 ) .
= 3 ( 1 + 2 − 3 ) .
= 3 ( 0 ) .
= 0 .
... and 0 is r a t i o n a l :D
The answer is 0, which is a rational number. :D
I think, my reasoning is so bad ( I can't explain it completely (like for instance, using some lemma, and stuffs) but, uhm, what if the question is
"Is i − i an imaginary (complex) number or real number ? "
What is the answer then? :)
Are you saying you don't know how to simplify "i - i" ?
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Nope sir, it's just you know, like illogical to subtract an imaginary number to another imaginary number. XD (they are both imaginary, I am just thinking that, is the operation of subtraction really applies to imaginary (complex) numbers ? Is there a lemma about it? )
N ⊆ Z ⊆ Q ⊆ R ⊆ C
i − i = 0 is real, therefore it is also complex (and a member of all the above sets) because they are subsets of each other.
This problem talks about rationals and irrationals, which are complements (I believe). All rationals (by definition) are rational, and by the subset property therefore all integers and naturals are as well.
Hope you can understand!
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I see it now sir. XD Thanks. ^^
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I am 16, like you. No need for 'sir' :)
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@Arthur Conmy – Oh, I didn't notice that, sorry. :D
root 3 + 2root 3 - 3root 3 =3root3-3root 3= 0, Zero is rational number.
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3 , 1 2 , 2 7 Note that all of the numbers above are multiple of 3 .
1 2 2 7 = 3 ∗ 4 = 3 ∗ 4 = 2 3 = 3 ∗ 9 = 3 ∗ 9 = 3 3
So 3 + 1 2 − 2 7 = 3 + 2 3 − 3 3 = 3 3 − 3 3 = 0
Therefore the answer is rational.