Before we attempt to simplify the given radical expression, let's consider one of the more difficult parts of correctly simplifying radicals. When the exponent of a variable inside the radical is even and the simplified expression for that variable has an odd exponent, we need to use absolute value symbols.
ll
sqrt(x^2)= |x| & sqrt(x^3)=x sqrt(x)
sqrt(x^4)= x^2 & sqrt(x^6)=|x^3|
This is because we do not want the result to be negative — the range of a square root function is all real numbers greater than or equal to 0. Now, consider the given radical expression.
sqrt(99ab^5c^2)
The exponent of b is odd, so we will not need absolute value symbols when we remove b from the radical. The exponent of c is even and, in the simplified expression, this variable will have an odd exponent. Therefore, when we remove c from the radical, we will need absolute value symbols.
Now that we have simplified the factors as much as possible, let's recall the Product Property of Square Roots.
sqrt(a* b)=sqrt(a) * sqrt(b), for a≥ 0,b≥ 0
Let's use this property to simplify our expression even further.
