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Q: What is the principal square root of a positive real number is always sometimes or never a negative?

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Yes. But NOT always.

it's only negative if it's being multiplied by a positive number. If it's being multiplied by another negative number than it will be positive.

no sometimes there positive i

Sometimes.* If "n" is positive, "-n" is negative. * If "n" is negative, "-n" is positive. * If "n" is zero, "-n" is also zesro.

sometimes

It is always positive, and not just for decimal numbers but for all numbers.

No. A positive times a negative is always negative. A negative times a negative is always a positive.

never

Depending on how you define it. Momentum is always given positive units, but sometimes when considered in a relative view, it can be in a negative direction making the overall value negative too (while mass is always positive, velocity might be in a negative direction where e.g. two masses are moving in opposite directions).

Yes, a negative number subtracted from a positive number will always be positive. Subtracting a negative number is the same as adding the opposite of the negative number. The opposite of a negative number is always positive. A positive number plus a positive number is always positive.

The answer is always positive. If the signs are the same (positive by positive, negative by negative), then the quotient is always positive. If the signs are different (positive by negative, negative by positive), then the quotient is always negative.

-12A negative times a positive is always a negative.A negative times a negative is always positive.

The square of a number is always two numbers multiplied together. A positive times a positive is always positive, and a negative times a negative is always positive.

In multiplication and division: always. In addition: never. In subtraction: sometimes.

always a positive

They are always negative due to a negative plus a negative equaling a negative. It's similar to a positive plus a positive equaling a positive.

Opposite of positive number will always be a negative number. The total of the two has to be zero as per the definition. So the zero does not have the opposite number.

No, two negatives multiplied together always form a positive number.

The product of negative number and a positive number is always a negative. The product of two positive numbers, or two negative numbers, is always a positive.

Always positive.

If the are always smiling then they are positive but if the are always perky then they are negative

A positive number multiplied by a negative number will always result in a negative number.

3

No, a positive minus a negative can be either or positive or a negative.

There is no such thing as a positive or a negative zero. A negative divided by a positive is a negative, and a positive divided by a negative is a negative. If you have a negative and a positive, the answer will be a negative. But if you have two negatives or two positives as the dividend and divisor, the answer will be a positive. In other words, dividing two positives or two negatives will always give you a positive. But dividing a positive and a negative will always give you a negative.