Question

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

Answer 1

`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)`