Verified answer

yes, √49 = only 7.

although (-7)^2 = 49, √ is called the principal root.

If it is a principal root, then the answer is positive.

However, -√ is called the negative root, so then the answer is negative.

-√49 = -7.

hope this helps! :)

Your math teacher is correct.

As a math teacher, I myself spend some time of my first period explaining this point to my students with examples.

Let me explain.

All square-roots are, by definition, positive unless a negative sign appears in front of it. Thus, √49 = 7 and - √49 = - 7.

This is because any representation of a number must be unique. Otherwise it can lead to problems. If √49 = ± 7, then - √49 = ± 7 which would mean that there is no diffrence between √49 and - √49

which => √49 = - √49 => 2√49 = 0 which is absurd.

Next question is what is √(x^2) ? Is it x or - x. Now, you may be tempted to say x and not - x. But this is also incorrect. If x is negative, you will end up getting a negative answer with x. Correct answer is

√(x) = l x l, which means that irrespetive of x being positive or negative, √(x) being modulus of x will be positive as is required by the definition of square-root.

Also, √(sin^2 x) = l sinx l which is sinx for x in 1st and second quadrants and - sinx if x is in 3rd or 4th quadrant.

If you have to solve an equation, x^2 = 49, it is

x^2 = 49 => x = ± √(49) = ± 7.

Steps

x^2 = 49 => x = √(49) = ± 7 will be incorrect

because √(49) = 7 and not ± 7.

It's amazing how many people do not understand what √ means.

√49 = 7, and NOT -7.

It is true that (-7) * (-7) = 49, so -7 IS a square root of 49, as well as 7. However, √ means only the positive root. This is why we use the symbol ±.

√49 = 7

-√49 = -7

±√49 = ±7, that is, -7 or 7.

Squareroot49=7.

the two roots of the equation

x^2 = 49 <=> x^2 - 49 = 0

are 7 and -7.

you can't interpret it another way.

The answer is only 7

Because if you take modulus of sqrt 49, we can write it as sqrt(7-0)^2 which is equal to modulus of 7 equal to 7

Hence, -7 does not satisfy as the squareroot of 49

Ok √49 = +7 or -7

Ok the reverse of a square root is the number to the power of 2

-7 * -7 = 49

and

7 * 7 = 49.

So

√49 = 7,-7

Also note that this can be written as √49 = + or - 7 (one on top of the other)

But there is a BUT

But if your doing certain types of maths.

For example logarithms , you wouldn't have a negative number as the answer because if so, the equation would be undefined => the answer is 7

If that logarithm made no sense what so ever dis-regard.

But basically in certain circumstances the negative number is disregarded.

Your math teacher is correct. √49 = 7. Why do you think we use the ± symbol? That shows when a square root can be either positive or negative. Without it, √(x) takes its principal value, which is always non-negative (see the graph of √(x)).

It depends on the level of mathematics you are doing. If you are 12, and first learning about square roots etc etc, then you should assume that the squareroot of 49 is only 7. However, in a few levels higher, you need to know that the square root of 49 is both 7, and -7.

You put both + and -, usually you write it with the + on top of the - and then 7, because they are both correct. Actually you can some times loose marks if you don't. 7X7=49 but -7X-7=49 also because a negative number times a negative number gives a positive.