is always positive irrational + positive irrational = irrational?

2 ⤊

is always positive irrational + positive irrational = irrational?

can I prove that there are two positive irrational numbers that their sum is rational? (please remember that there is no negative numbers in this case).

2007-05-08 08:13:13 · 3 answers · asked by master343 3 in Science & Mathematics ➔ Mathematics

3 answers

It's not true.

Consider the following:
(5-√2) + √2 = 5.

(5-√2) is positive and irrational, and it's about: 3.5857864
√2 is positive and irration, and it's about: 1.4142136

Their sum is 5, which is clearly a rational number.

2007-05-08 08:24:06 · answer #1 · answered by NSurveyor 4 · 1⤊ 0⤋

yes

2007-05-08 08:18:14 · answer #2 · answered by pioneers 5 · 0⤊ 1⤋

no

[10+sqrt(2)]+[10-sqrt(2)]=20

.

2007-05-08 08:22:39 · answer #3 · answered by gjmb1960 7 · 1⤊ 1⤋