Question 964354: How do you solve this? : sqrt(1-a^2)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this is not an equation.
it's an expression.
as an equation it would have to be equal to something, like sqrt(1-a^2) = 5.
by itself it has no solution.
the best you can do is find the values of a that would make the solution real.
since the square root of a number has to be greater than or equal to 0, then you get:
1 - a^2 >= 0
add a^2 to both sides of that equation to get 1 >= a^2
that's the same as a^2 <= 1
in order for the solution to be real, a^2 must be smaller than or equal to 1.
when does that happen?
set a^2 equal to 1.
solve for a by taking the square root of both sides of this equation to get:
a = plus or minus sqrt(1) which becomes a = plus or minus 1.
so a^2 = 1 when a is equal to plus or minus 1.
what happens when a is greater than 1.
a^2 is greater than 1, so a can't be greater than 1.
what happens when is is smaller than -1.
a^2 is greater t han 1, so a can't be smaller than -1.
that happens when a is between -1 and 1.
a^2 is less than 1.
bottom line is -1 <= a <= 1 is when the solution will be real because a^2 will then be less than or equal to 1 and the square root of (1-a^2) will therefore be greater than or equal to 0.
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