Square Root Graph Question (1 Viewer)

[Ambility]

Why is the graph only above the x-axis? Shouldn't this have a mirror reflection below the x-axis?

For example, the square root of 25 is 5, but also -5. Why is this not in the graph?

 

[leehuan]

False.

The square root of 25 is 5.
√25 = 5

But the equation x^2 = 25 has two solutions
|x| = 5
x = ±5

Note that -√25 = -5. When we take the square root OPERATOR we only consider the principal root.
But the quadratic EQUATION will have two solutions.

 

[leehuan]

Additionally, consider the graph of x = y^2

This is a sideway parabola.

But the graph of y = √x is only the top branch of it.

 

[Ambility]

False.

The square root of 25 is 5.
√25 = 5

But the equation x^2 = 25 has two solutions
|x| = 5
x = ±5

Note that -√25 = -5. When we take the square root OPERATOR we only consider the principal root.
But the quadratic EQUATION will have two solutions.

Are you saying that this calculator is incorrect? http://www.calculatorsoup.com/calculators/algebra/squareroots.php

 

[leehuan]

Are you saying that this calculator is incorrect? http://www.calculatorsoup.com/calculators/algebra/squareroots.php

Read what I said. The operator relates to the PRINCIPAL root.

If we were to sketch the graph of ALL of the roots it would be crazy. Tbh, in fact incorrect.

There is a huge distinction between the value of √25 and the solutions to the equation x^2=25

 

[Nailgun]

From your calculator webpage lol

Any nonnegative real number x has a unique nonnegative square root r; this is called the principal square root .......... For example, the principal square root of 9 is sqrt(9) = +3, while the other square root of 9 is -sqrt(9) = -3. In common usage, unless otherwise specified, "the" square root is generally taken to mean the principal square root."[1].

 

[InteGrand]

Why is the graph only above the x-axis? Shouldn't this have a mirror reflection below the x-axis?

For example, the square root of 25 is 5, but also -5. Why is this not in the graph?