Is this true??????????????????????
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# Is this true??????????????????????

[From: ] [author: ] [Date: 11-10-07] [Hit: ]
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).The sum (or difference) of any two irrationals may be irrational or rational.i.......
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?

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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,