Karl says that you can take the square root of each side of an equation. Therefore, he says

Question

that (x + 5)2 + ( y – 7)2 = 36 and ( x + 5) + ( y – 7) = 6 are equivalent equations. Emily says the equations are not equivalent. Who is right? Explain your answer.

I know Emily is right, but how?

Answer 1

If you take the square root of 36x^2 you will get 6x. This is fine because you only have one term.

But, if you take the square root of
36 - x^2, you can't take the square root of each part when you are adding or subtracting which causes you to have more than one term. The answer is NOT 6 - x.
Try this with numbers. Suppose x = 2
36 - 4 = 32 and the square root of 32 does not equal square root of 36 - square root of 4
So 6 -2 is not 32.

I hope this helps.