I read in manhattan GMAT book as even root of a number results only +ve but not -ve in GMAT.
example:-
if x=sqrt64 then x=8 but not -8
Many other books and material always mentions like
if x^2=64 then x=+1/-1
which is correct? did I misunderstand any?
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- RonPurewal
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Those are both correct.
THE SQUARE ROOT SYMBOL ITSELF carries the implicit meaning of choosing the positive root. This is so because symbols - which represent FUNCTIONS - can't take on more than one value; therefore, the symbol is DEFINED to take on the positive ('more useful') value.
In the equation x^2 = 64, there is no use of the square root symbol. This is an EQUATION which is allowed to have multiple solutions (it's not a FUNCTION of x). Therefore, we are after ALL x's that will solve it (two of them, in this case).
By the way, I certainly hope that your books aren't telling you that 1 and -1 are solutions to x^2 = 64 (the correct answers, of course, are 8 and -8). If they are, oh dear...
PS If you know trigonometry, this is the same reason why arcsin(1/2) is ONLY defined to be 30 degrees, but tons of x's solve the equation sin x = 1/2 (like 150, 390, -330, and so on). If you don't know trigonometry, then ignore this example, but pay attention to the text above.
THE SQUARE ROOT SYMBOL ITSELF carries the implicit meaning of choosing the positive root. This is so because symbols - which represent FUNCTIONS - can't take on more than one value; therefore, the symbol is DEFINED to take on the positive ('more useful') value.
In the equation x^2 = 64, there is no use of the square root symbol. This is an EQUATION which is allowed to have multiple solutions (it's not a FUNCTION of x). Therefore, we are after ALL x's that will solve it (two of them, in this case).
By the way, I certainly hope that your books aren't telling you that 1 and -1 are solutions to x^2 = 64 (the correct answers, of course, are 8 and -8). If they are, oh dear...
PS If you know trigonometry, this is the same reason why arcsin(1/2) is ONLY defined to be 30 degrees, but tons of x's solve the equation sin x = 1/2 (like 150, 390, -330, and so on). If you don't know trigonometry, then ignore this example, but pay attention to the text above.
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