How do you simplify square root of three to the 15th power?
sqrt((3^15))
1 Answer
Jan 27, 2018
Explanation:
The question is slightly ambiguous in that it could mean either of the following:
-
Take the square root of
3 then raise it to the15 th power, i.e.(sqrt(3))^15 -
Raise
3 to the15 th power then take the square root, i.e.sqrt(3^15)
In general if
So we find:
sqrt(3^15) = sqrt((3^7)^2 * 3) = 3^7 sqrt(3) = 2187 sqrt(3)
Also:
(sqrt(3))^15 = (sqrt(3))^14 sqrt(3) = ((sqrt(3))^2)^7 * sqrt(3) = 3^7 sqrt(3) = 2187 sqrt(3)