How do you simplify 3sqrt(27x^7)?

1 Answer
Mar 14, 2018

9x^2sqrt(3x^3)

Explanation:

Rule: group things inside the square root in groups of 2 so you can "take them out" of the square root

sqrt(27) can be written as sqrt(3*3*3). Now "take it outside the square root 3*sqrt(3)

Then do the same thing for x^7. Recall the rules for exponents and how they add i.e. x^2*x^2 is equal to x^4

So x^7 rewritten in groups of 2 would be x^2*x^2*x^3. Since we can take those two groups out, it becomes x^2*sqrt(x^3)

Now combine 3*sqrt(3) and x^2*sqrt(x^3) so you get 9x^2sqrt(3x^3)