simplify sqrt(9x^2+18x+9) - inside the square root is a perfect square

Question

simplify sqrt(9x^2+18x+9) - inside the square root is a perfect square

Answer 1

Hi Jimmy, there are several approaches to this problem. Here is one of them.

 

Consider what is inside of the brackets alone:

 

9x² + 18x + 9

 

All three terms contain a nine or multiple of nine, so we can take a nine out of each term leaving:

 

9 * (x² + 2x + 1)

 

Now, working with just x² + 2x + 1, we can factor this:

 

(x + 1) * (x + 1) = (x + 1)² 

 

Now, return to the solution of the square root:

 

√( 9 * (x + 1)² )

 

3 * 3 = 9, so we can take 3 out from under the radical

 

We have show above (x + 1) * (x + 1) = (x + 1)², so we can take the (x + 1) out from under the radical.

 

The solution is:

 

√( 9 * (x + 1)² ) = 3 * (x + 1), or 3x + 3

 

Questions?

Answer 2

√(9x²+18x+9) = √[9(x²+2x+1)]

 

                     = √[9(x+1)²] = 3(x+1) = 3x+3