1) Sqrt(2) + sqrt(2) = irrational. This is true right?
2) Sqrt(2)  sqrt(2) = rational, because the answer is 0 and 0 can be expressed at a/b, where a and b are integers and b DNE 0.
I think the first statement is true right? Is there a case where you add 2 irrational numbers you get a rational number?
2) Sqrt(2)  sqrt(2) = rational, because the answer is 0 and 0 can be expressed at a/b, where a and b are integers and b DNE 0.
I think the first statement is true right? Is there a case where you add 2 irrational numbers you get a rational number?

Hello,
√2 + √2 = 2√2
It is indeed an irrational value.
You have to understand that, in the great scheme of things, addition and subtraction are one and the same.
substraction = addition of the opposite.
Hence, yes, there is a case where adding two irrationals you get a rational.
(√2) is irrational.
Thus (√2) is also irrational.
Hence the sum of one irrational (√2) and another irrational (√2) can yield a rational (0).
Or said in another manner:
The sum (or difference) of any two irrationals may be irrational or rational.
i.e. There are not rule about "being irrational or not" and "addition or subtraction".
= = = = = = = = = = = = = =
And if you are not convinced:
Try to compute with a calculator:
cos²(π/8) ≈ 0.85355339059327376220042218105242
sin²(π/8) ≈ 0.14644660940672623779957781894758
I don't have to explain to you how much is their sum... Mmmm?
cos²(π/8) happen to be irrational and sin²(π/8) too.
Because actually,
cos(π/8) = √(2 + √2) / 2 and sin(π/8) = √(2  √2) / 2
cos²(π/8) = (2 + √2) / 4 and sin²(π/8) = (2  √2) / 4
Logically,
Dragon.Jade :)
√2 + √2 = 2√2
It is indeed an irrational value.
You have to understand that, in the great scheme of things, addition and subtraction are one and the same.
substraction = addition of the opposite.
Hence, yes, there is a case where adding two irrationals you get a rational.
(√2) is irrational.
Thus (√2) is also irrational.
Hence the sum of one irrational (√2) and another irrational (√2) can yield a rational (0).
Or said in another manner:
The sum (or difference) of any two irrationals may be irrational or rational.
i.e. There are not rule about "being irrational or not" and "addition or subtraction".
= = = = = = = = = = = = = =
And if you are not convinced:
Try to compute with a calculator:
cos²(π/8) ≈ 0.85355339059327376220042218105242
sin²(π/8) ≈ 0.14644660940672623779957781894758
I don't have to explain to you how much is their sum... Mmmm?
cos²(π/8) happen to be irrational and sin²(π/8) too.
Because actually,
cos(π/8) = √(2 + √2) / 2 and sin(π/8) = √(2  √2) / 2
cos²(π/8) = (2 + √2) / 4 and sin²(π/8) = (2  √2) / 4
Logically,
Dragon.Jade :)

both your answers right
now as far as adding two irrationals
(1sqrt(2))+(1+sqrt(2))
is a example of adding irrational and getting rational
now as far as adding two irrationals
(1sqrt(2))+(1+sqrt(2))
is a example of adding irrational and getting rational