Question

Since Sqrt(x^2) = |x|, thus Sqrt((x+y)^2) =

A) x + y
B) |x + y|
C) x - y
D) |x - y|

Answer 1

Sqrt((x+y)^2) equals |x + y| as it represents the principle square root ensuring a non-negative result, similar to how Sqrt(x^2) equals |x|.

Step-by-step explanation:

The equation Sqrt((x+y)^2) is equal to |x + y|. This is because when you take the square root of a squared number, you end up with the absolute value of the original number, similar to Sqrt(x^2) which results in |x|. The square root and the square cancel each other out, but since we can't assume that x + y will always be positive, we take the absolute value to ensure the result is non-negative, in accordance with the principal square root definition.