Is the sum of two irrationals always an irrational number?
Is the product of two irrationals always an irrational number?
2006-06-27 14:23:02 · 5 answers · asked by stillborndesires01 1 in Science & Mathematics ➔ Mathematics
no:
sqrt(2) + (-sqrt(2)) = 0 rational
no
sqrt(2)*(1/sqrt(2)) = 1 rational
sqrt(2) and 1/sqrt(2) are irrational
In general , it's more often that sum ( product) of too irrational is irrational
2006-06-27 14:35:15 · answer #1 · answered by Theta40 7 · 0⤊ 0⤋
No and no. Given all rational numbers "a" and all irrational numbers "b", b and (a-b) are both irrational, yet their sum is rational.
To the second question, for a simple example, consider the square root of any non-square rational, which is always irrational, let's call it "c". Then any rational "d" multiplied by "c" is an irrational number. So "c" and "cd" are both irrational and their product is (c^2)d, which is the product of two rationals, therefore rational.
2006-06-27 14:43:09 · answer #2 · answered by untypicalman 1 · 0⤊ 0⤋
no. For instance you multiply squareroot of 2 (which is an irrational number) by another irrational number, itself. you will get a rational number which is 2. And also, you add e with -e which are bothe irrational, you will get 0 which is a rational number.
2006-06-27 14:36:56 · answer #3 · answered by meow 3 · 0⤊ 0⤋
The closure property does NOT hold for the irrational numbers under addition or multiplication.
2006-06-27 14:45:34 · answer #4 · answered by KHB 2 · 0⤊ 0⤋
hmmm... is the square root of 2 irrational? if you multiply it by the square root of 2.. you get 2.. so .. no.. if you multiply them.. the product is not always irrational... yes.. i think the sum is though
2006-06-27 14:34:28 · answer #5 · answered by ♥Tom♥ 6 · 0⤊ 0⤋