When taking the square root of both sides of the equation, how many solutions will the equation have? how do you know

  it depends

Step-by-step explanation:

An equation such as ...

  x² = 4

will have two solutions:

  x = ±√4 = ±2

Both of these solutions will satisfy the original equation.

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An equation involving distances, such as the one you get when using the Pythagorean theorem, will have one solution. The negative solution is extraneous, as negative distances don't exist.

  c² = a² +b²

  c = √(a² +b²) . . . . . positive root only

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An equation involving time, such as the one usually used to describe ballistic motion, may have two solutions that include a negative time solution. Generally, those are not useful, so are considered extraneous. Mathematically, negative time values work in the equation, but they have no interpretation in the real world.

An equation such as ...

  x⁶ = 4

will have two real solutions and 4 complex solutions.

  x³ = ±2 . . . . . after taking the square root of both sides

The two real solutions are ...

  x = ±∛2

How do you know?

a) try the solutions in the original equation to see how many give useful results

b) generally, for polynomials, the number of solutions is equal to the degree of the equation

c) consider the reasonable domain of the variable of interest

2 pecks

step-by-step explanation:

cause it equals more