How do you simplify ((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2))?

1 Answer
Elvan Burcu K.
Apr 9, 2015

For this kind of a question you should multiply the nominator and the denominator with the demonator but with the minus sign. (forgive me for my bad english :). What i mean is, this is what you should do;

((sqrt7)-(sqrt2))/((sqrt7)+(sqrt2)) since there is ((sqrt7)+(sqrt2)) in the denomintor you should multiply the whole equation with ((sqrt7)-(sqrt2))

The reason we do this to reach this result in the denominator part;
((sqrt7)+(sqrt2)) . ((sqrt7)-(sqrt2)) = 7 - 2 = 5
I came to that from this formula;
(x+y) . (x-y) = x^2 - y^2 => This is a formula that should be memorized in order to solve this kind of question.

Also you have to know this too;
(x-y)^2 = x^2 - 2xy + y^2

So if i solve the entire question the result will be;
((sqrt7)-(sqrt2))/((sqrt7)+(sqrt2)) = ((sqrt7)-(sqrt2))/((sqrt7)+(sqrt2)) * ((sqrt7)-(sqrt2))/((sqrt7)-(sqrt2)) = ((sqrt7)-(sqrt2))^2/(7-2) = (7-2sqrt14 + 2)/ 5 = (9- 2sqrt14)/5 => this is the simplest version i can write. I hope it helps.

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