Does sqrt(a^2 - b^2) = a - b ?
If so or not, why ?
2007-11-11 16:38:58 · 5 answers · asked by c0cky 5 in Science & Mathematics ➔ Mathematics
No. It can't be cancelled out because you are subtracting. This is the same as saying
sqrt(a+b)(a-b)
2007-11-11 16:48:18 · answer #1 · answered by YamiRob 2 · 0⤊ 0⤋
No. You can not use the square root like that with addition and subtraction. a^2 - b^2, if you were to factor it out, would be (a-b)*(a+b).
You can, however, use it like that for multiplication and division. Therefore: sqrt(a^2*b^2) = a*b
2007-11-11 16:46:32 · answer #2 · answered by starmandxe 1 · 0⤊ 0⤋
No, that is indeed a trap. Simply, it is against the rules of algebra. But...
sgrt(a^2 - b^2) =/ a-b ( =/ stands for "not equal to")
a^2 - b^2 =/ (a-b)^2
by squaring both sides, you should be able to see why.
2007-11-11 16:56:56 · answer #3 · answered by Anonymous · 0⤊ 0⤋
No.
Reverse it to check:
(a-b)^2 = (a-b) * (a-b)
= a^2 - 2ab + b^2
2007-11-11 16:47:57 · answer #4 · answered by Mark P 2 · 0⤊ 0⤋
nope.. sorry, if you factored ot out you'll just get
(a - b)*(a+b)
and is NOT a perfect square
2007-11-11 17:00:38 · answer #5 · answered by windzard 2 · 0⤊ 0⤋