Roots and Signs

[shartjen]

Hi,

doing the practive exams one Manhattan prep, I have encountered a question and its answer that I am insecure about.

Compare A-B question:

A: Cubic root(18*12)

B: Squareroot (18*2)

The factors do match after calculation. Thus Manhattan answer:
C They are equal

My question isn't B +/- 6 and wouldn't D apply, cannot be determined?

Am I to messed up by too many questions today? Are squareroots of numbers always positive for GRE-purpose. Do I miss anything else. Is C the right answer for sure?

[n00bpron00bpron00b]

Answer "C" is correct

Quantity A

Cube root of (18*12)
Cube root (3x3x2x2x2x3)
Cube root (27x8)
=> 3 x 2 = 6

Quantity B
Square root of (18*2)
Square root of (2x3x3x2)
=> Square root of (4x9)
=> 2x3 = 6

Both equal.

For Square root's or any even roots (like 4,6,8,10...) there are 2 cases -

case 1

When you see values under "square root or even root symbol" also called as principal root -> always consider only the positive value

case 2

When you simplify even exponential values like x^2, x^4, x^6 ... always consider both positive and negative values

ex. square root of 4 is strictly positive 2 where as -
in the equation x^2 = 4 => the value of "x" is +2 or -2

You don't have to worry about sign for odd exponents/roots (like cube, fifth, and so on..)

[tommywallach]

Indeed. Square roots of NUMBERS are always positive. The only time you have to worry about pos/neg solutions is when you take the square root of a value with an unknown/variable in it.

-t