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

1 Answer
Mar 14, 2018

Answer:

#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)#