pemdas wrote:@Nil, you misinterpreted
i don't disagree and know beforehand what you were typing and all in red ...
what I mean is that sqrt(x^2)=|x| is true for any value of x within absolute
sqrt(9) has two roots: primary and secondary, i.e. |3|=+-3 (+ve and -ve) - Partly agree
when it stated sqrt(9)=-3 would be different from sqrt(x^2)=-x, as x has two signs within its modes (+ve and/or +ve), then we can switch the signs ...
that's the whole point, both statements include radicals with squares and it's Insuff for both statements together to have -3 as solution, because 3 is also solution here.
It's not right when you put sqrt(-9) but this it right when it's sqrt(9)=-3, conversely sqrt(9)=+3, since -3^2=9 and +3^2=9
I hear what you are saying! My understanding of definition of square root in GMAT (from expert posts on GMAT problems/and solutions provided by Prep companies), Square root of a number is the principal square root which is the positive square root.
Every positive number x has two square roots: , which is positive, and , which is negative. Together, these two roots are denoted (see ± shorthand). Although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root. - Source Wiki
So,
the statement sqrt(9) has two roots: primary and secondary, i.e. |3|=+-3 (+ve and -ve) is correct BUT In general and in GMAT sqrt(9) = 3 and not
+3
Check the Properties section here ->
https://en.wikipedia.org/wiki/Square_root and if you agree to the definition of Square root(x^2) as provided there, then you should agree that
sqrt(9) = 3 and not
+3 because if you assume
9 = -3*-3, then sqrt(9) = sqrt(-3^2) = -(-3) = 3 (Definition: sqrt(x^2)= -x if x < 0.)
and if you assume
9 = 3*3, then sqrt(9) = sqrt(3^2) = 3 (Definition: sqrt(x^2)= x if x
> 0.)
p.s: I am sorry if your question is still left unanswered, but I s**k at explaining things and I am trying to improve in that region.
-x is -1*x. You cannot disagree with sqrt(x^2)=|x| correct?
