How do I simplify to ?

Thanks :)

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- January 25th 2008, 09:49 AMslevvioSurd
How do I simplify to ?

Thanks :) - January 25th 2008, 11:13 AMSoroban
Hello, slevvio!

Quote:

First, we must*suspect*that is a square.

Then we let: .

. . where both are*rational*numbers.

Square both sides: .

. . and we have:. .

These two numbers are equal if their corresponding coefficients are equal.

So we have: .

The second equation gives us: .

Substitute into the first equation: .

Multiply by

. . which factors: .

. . and has roots: .

Since must be rational and the original square root is positive,

. . the only acceptable root is: .

Therefore: .

- January 25th 2008, 11:54 AMKrizalid
- January 27th 2008, 09:49 AMSoroban
Hello, Krizalid!

Of course, you are right . . . That is a valid method.

I use that method when I'm quite certain that we have a square.

I've done it enough times that I suspect that is a square

. . because: .

And, sure enough: .