Cubing Y from X

[am.harel]

This question is from the Question bank on number properties, which asks:

If x is not equal to y and if x^(1/2)=y , what is the value of y^3 ?

(1) x = y^x

(2) x^3 = 8

The explanation says that both are sufficient (D) since the algebra lets you figure out that x=2. However, if you know x equals 2, then can't y technically be either the positive or negative square root of 2. And if that is raised to the 3rd power, won't it still carry the same sign, indicating that there are two possible values for y^3?

[pranabiitkgp]

Square root of 2 is always positive .
Like square root of X^2 is always X and not +/- X , OR other way to treat this as mod , so square root of X^2 is mod X or |X|.

But if we have a euation as X^2 = Y^2 , then you can say X=+/- Y.

Hope this will clarify.
Thanks,
PM.

[tim]

the best way to think of this is that if the problem gives you a square root sign (or an exponent of 1/2), you will take only the positive value. if you insert the square root sign yourself, you need to consider the positive and negative values..