Find the following. Assume that variables can represent any real number.
SqRt(a+8)^2=
8a^2?
sqrt[(a+8)^2] = a+8 or -a-8
No, when we take the sqrt of a squared term, we get that term, or its negative.
So, sqrt(x²)=x or sqrt(x²)=-x
So for this question we get that:
sqrt((a+8)²)=a+8 or sqrt((a+8)²)=-a-8
To find the value of the expression "√(a+8)²," you can follow these steps:
1. Simplify the expression inside the square root:
(a + 8)² = a² + 2·a·8 + 8²
= a² + 16a + 64
2. Take the square root of the simplified expression:
√(a² + 16a + 64)
However, you mentioned that the possible answer given is "8a²." We can check whether this is true by squaring it and comparing it to the original expression.
Squaring 8a²:
(8a²)² = 64a⁴
Now, let's compare it to the original expression:
√(a² + 16a + 64) vs. 64a⁴
Since the two expressions are not equal, we can conclude that "√(a+8)²" is not equal to "8a²."