If 3^2=9 and the square root of 9 can be -3, then surely 3 can = -3.
2006-06-20 06:44:13 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A square root cannot be negative. It's true that -3 * -3 = 9, but the square root is defined as 3 and not -3.
Even if you were right though, you wouldn't break mathematics. You'd just discover something interesting :)
2006-06-20 06:49:14 · answer #1 · answered by mike_w40 3 · 0⤊ 0⤋
You left out an important detail. The square root of 9 is the absolute value of 3 or |3| which equals 3 or -3. 3 does not equal -3, the absolute value of 3 and -3 = 3.
2006-06-20 06:51:44 · answer #2 · answered by answer lady 2 · 0⤊ 0⤋
Yes, square root of 9 does equal +-3 BUT don't forget that square root of 3^2 yields +-3.
Also using another analogy, you can reject the roots that don't work. Same as solving an equation with multiple roots; you simply ignore the incorrect ones. In this case, you'll be rejecting -3. Hope that helps.
2006-06-20 08:04:06 · answer #3 · answered by ready_to_rumble 1 · 0⤊ 0⤋
No, the square root of 9 can't be -3. But the solution to the equation x^2 = 9 isn't x = root(9), but x = +- root(9), which means that x can be either root(9) or -root(9).
2006-06-20 06:57:45 · answer #4 · answered by User1 2 · 0⤊ 0⤋
You basically made this claim (but in math):
A dog is an animal, but a cat is also an animal. Therefore a dog is a cat.
x^2 is not a one-one function. That means that 3^2 is always equal to 9, but 3 is not the only number thats square equals 9.
Just like the animal argument. Defining something as an animal is not 1-1. Every dog is an animal, but not every animal is a dog.
2006-06-20 07:00:19 · answer #5 · answered by Eulercrosser 4 · 0⤊ 0⤋
no. Because you are taking two different things and putting them together.
if you have x²=9, then you get x=3 or x=-3. But that means there are two possible solutions, not that 3=-3.
2006-06-20 06:52:39 · answer #6 · answered by bequalming 5 · 0⤊ 0⤋
If turning right twice at right angle, and turning left twice at right angle, give you the same result, then surely left is the same as right.
2006-06-20 06:58:06 · answer #7 · answered by ringm 3 · 0⤊ 0⤋
The function f(x) = x^2 is not one to one, meaning that there can be two numbers x1 and x2 such that f(x1) = f(x2).
2006-06-20 06:54:10 · answer #8 · answered by blahb31 6 · 0⤊ 0⤋
No. -3 is not equal to +3. But I-3I = I+3I. (-ve)*(-ve) = (+ve) and (+ve)*(+ve) = (+ve). ie. (-ve)^2=(+ve)^2=(+ve).
(-ve)^2=(+ve)
((-ve)^2)^0.5)=(+ve)^0.5
(-ve) = (+ve) or (-ve)
2006-06-20 21:11:15 · answer #9 · answered by K.J. Jeyabaskaran K 3 · 0⤊ 0⤋