How do you know whether a square root is plus or minus?

Question

Sometimes when you square a number, the answer is plus or minus the answer, but sometimes it's not, sometimes it's only a positive or negative number, I don't understand that.

Answer 1

Hi,

Everytime (100%) of the time, when you take the square root of a number, it will be plus/minus the square root value.

For example, if we take the square root of 4, we get 2 and -2 and here's why:

2 x 2 = 4

-2 x -2 = 4

Since two positive numbers multiplied by eachother give a positive number and also two negative numbers multiplied by eachother give a positive number, we therefore need to account for the plus/minus!

I hope that helps you out! Please let me know if you have any other questions!

Sincerely,

Andrew

Answer 2

The short answer is:

* If you are given just an equation, the correct answer is to find all (both) of its solutions.
* If you are given the word problem behind the equation, the correct answer is to find all (both) of the math solutions, then decide which solution(s) make sense with the word problem.

This happens because the math we use is not always perfect model of the problem we're trying to solve. So sometimes the math gives us multiple solutions, but then we have to go back to the original word problem to decide which of the solutions make sense.

A simple example: The label on a can of paint says that it will cover 90 square feet. I want to know: what is the diameter of the largest circle I can paint?

I use the formula:

Area of circle = πd²/4 = 90 sq.ft.

Now it turns out that there are TWO values of "d" that will satisfy this equation:

Solution 1: d = sqrt(360 sq.ft./π)
Solution 2: d = –sqrt(360 sq.ft./π)

And you can verify by plugging both those values in, that each one really does satisfy the equation. However, since we know from the original word problem that "d" is supposed to be a diameter of a circle, the negative solution does not make sense here; so we discard it and use only the positive solution.

Note that, if all we were given were just the equation, and we weren't told what the word problem was, we would have to say that "d" has two possible solutions. But when we DO know the word problem, that acts like an additional constraint on the math; and (sometimes) means that we should discard one or more of the equation's solutions.

Answer 3

for real numbers (x)^2 = x^2 and (-x)^2 = x^2, i.e., the sqaure is a positive value. It is not negative.

Conversely, taking the square root means that the value can be positive or negative. In econonic or physical applications, sometimes the negative value has no meaning; hence it's rejected, and only the positive value is used. So while the mathematical validity of the negative value is not questioned, it must be taken in the context of the actual problem.

Answer 4

Any positive number has two square roots, one is positive and one is negative. For example, both 3 and -3 are square roots of 9 since if you multiply either one by itself you get 9.

Which of the two square roots you need depends on the problem. Often only one makes sense. Sometimes both will work, and you get two solutions!

Answer 5

are you able to positioned up an occasion? interior the quadratic formula, there's a 'plus or minus' in front of the sq. root, on account which you may have 2 distinctive values which paintings... different than that, in case you may have a -x as a term in an equation or assertion, then you may have a detrimental in front of a sq. root besides... the fee of the sq. root oiperation is basically a term interior the expression or equation...

Answer 6

a square root cannot be said whether it's a negative or positive. but for sure, a negative number cannot be used in square root

Answer 7

When there is a negative sign IN FRONT of the square root box, that makes it negative. When there is an positive and a negative sign, it is both. When there isn't any sign, it is always positive. Hope that answers your question.

Answer 8

You cannot square numbers into negatives. It is impossible. Any two positives multiplied will equal a positive. Also, any two negatives will equal a positive.

Answer 9

when we are talking of square roots, you'll always be dealing with the principal square root which is positive (ALWAYS). On the other hand, when you're talking about something like x² = something then it would be ±√something...

Answer 10

The mathematical answer always is plus or minus

But usually the application can only accept one