help please. hw assignment and i d k
2007-11-08 10:01:22 · 4 answers · asked by answersanonymous 3 in Science & Mathematics ➔ Mathematics
radical 3 is not rational.
Proof: if a number is rational, it can be written as a fraction in lowest terms, a/b, where there is no number that divides into both a and b
Let radial 3 = a/b
Then, squaring, 3 = a^2/b^2
So a must be divisible by 3. But any square that is divisible by 3 is divisble by 9. So b^2 is divisible by 3 ... You quickly find that b^2 is divisible by 9 and both a and b are divisible by 3.
This contradicts the assumption that a/b is in its lowest terms.
So we can't find a fraction a/b = radical 3
It is said that a disciple of Pythagoras discovered this (for radical 2, where the same reasoning applies), and was so horrified that he committed suicide.
2007-11-08 10:17:25 · answer #1 · answered by Facts Matter 7 · 1⤊ 1⤋
Rational Radical
2016-12-12 06:33:00 · answer #2 · answered by ? 4 · 0⤊ 0⤋
Rad 3 is not rational because a rational number is one that ends or repeats. Since Rad 3 goes on forever and ever, it does not terminate so it is irrational.
If this helped you, a best answer would be greatly appreciated!
2007-11-08 10:08:09 · answer #3 · answered by guitarman 2 · 1⤊ 0⤋
no, radical numbers are intergers (whole) or can be written as a fraction (or ratio of intergers)... the square root of 3 is not rational, it is irrational
2007-11-08 10:05:22 · answer #4 · answered by luisfernu@sbcglobal.net 2 · 1⤊ 0⤋