Important question on roots and exponents

Question

On the GMAT we are told by the GMAC that: the value of \(4^2\) has two values, +2 and -2. However the value of Square root of 4 has only one value, 2.

However, 4^1/2 equals square root 4. So my problem is, when you translate between fractional exponents and roots, what happens with the rule?

If the GMAT write down 4^1/2, does that mean if I translate it to square root 4 I only have 1 answer? Because 4^1/2 sorta has two answers. Or is it that you always need to translate 4^1/2 into square root 4 because its not proper to have fractional exponents?

Someone help, thanks

bb · Answer

On the GMAT you are only tested about the positive results of square root operations, so \(\sqrt{4}\) has only one solution - 2

This does make things a bit funny, and most don't even think/know about this. However, it is a wall for mathematically inclined to climb over

jeckll · Answer

4^2 (4^2) has only one value: 16 I think you mean \sqrt{4} :wink:

benjiboo · Answer

Here is my problem:

X^2  has two solutions, one positive and one negative.

|X| has two solutions, one positive and one negative

\sqrt{X^2}  = |X|

However, GMAT states that  \sqrt{X}  has only one solution, the positive value.

SO...

\sqrt{25}  = 5

but according to the GMAT

\sqrt{5^2}  = 5 and -5

yet 25 =  5^2

I am confused! Help?

hgp2k · Answer

I am confused too now. So according to GMAT  \sqrt{x}  has only positive value?????

srini123 · Answer

check this link https://www.mathpath.org/concepts/princ ... e.root.htm it talk about principal square root, is that it for GMAT too, GMAT considers only principal square root?

Important question on roots and exponents

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