Is Square Root = Always Positive? GMAT Problem Solving

Question: Is Square Root = Always Positive?

1.  Yes
2.  No
3. Not Always

“Is Square Root = Always Positive?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer: C

Explanation: It is asked Is Square Root = Always Positive?

This is a tricky question

The mathematical function known as the square root really goes by the term positive square root function and produces all positive values, as would be expected. This distinction is made because in a mathematical function f(x, y), there must be a separate value of y for each value of x. Therefore, by definition, the square root of 4 cannot be +2, -2! Therefore, we only consider the square root function to be positive as a rule.

Because the square of both +2 and -2 is 4, but the square root of 4 can only take the value of +2, this leads to a lot of confusion, but that is the set of rules that we follow.

The square root of any number is essentially that number multiplied by itself, up to the largest possible number. As an illustration, the square root of 16 is 4, so 4 times 4 equals 16.

But there are other square roots for the number 16. By the same reasoning that the same number must be multiplied together to produce the larger number, -4 times -4 likewise equals 16.

The answer to the question , the square root of a square number is NOT ALWAYS positive. It is just the most widely used answer.

A "primary root" is "a real number, preferably a non-negative one,"

An example would be

The principal square root of 25 is 5.
The square roots of 25 are 5 and -5.

Another example

\(x^2\) = 49

\(x^2\) = √49

x = |7|

Now,
since 7 is in an absolute value form, it can be a positive or a negative

The answer is C , not always

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