Simplify: sqrt(72x^3)-5x sqrt(2x)
I need all of the steps.
I need this ASAP because this assignment is due tomorrow.
Thanks
To simplify the expression sqrt(72x^3)-5x sqrt(2x), we can follow these steps:
Step 1: Break down the numbers inside the square roots into their prime factors.
72 can be split as 2*2*2*3*3, and x^3 can be written as x*x*x.
So, sqrt(72x^3) becomes sqrt(2*2*2*3*3*x*x*x).
Step 2: Rearrange the factors inside the square root.
Rearrange the factors inside the square root to group the square numbers separately from the non-square numbers.
sqrt(2*2*2*3*3*x*x*x) becomes sqrt((2*2)*(2*3)*(3*x*x*x)).
Step 3: Simplify the squared factors.
The square factors, (2*2) and (3*x*x*x), can be taken out of the square root because square roots undo squares.
sqrt((2*2)*(2*3)*(3*x*x*x)) becomes (2*3*x) * sqrt(2*3).
Step 4: Evaluate the remaining expression without the square root.
Simplify the expression (2*3*x) * sqrt(2*3) by calculating the multiplication outside the square root.
(2*3*x) * sqrt(2*3) becomes 6x * sqrt(6).
Step 5: Simplify further if possible.
To simplify the expression completely, we can check if any common factors exist between 6x and sqrt(6). However, there are no common factors, so the final result is:
6x * sqrt(6)
Therefore, the simplified expression is 6x * sqrt(6).