Answer:
Factor 10 into its prime factors
10 = 2 • 5
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
In our case however, all the factors are only raised to the first power and this means that the square root can not be simplified
At the end of this step the partly simplified SQRT looks like this:
sqrt (10p3)
STEP
2
:
Simplify the Variable part of the SQRT
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt(x8)=x4
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) sqrt(x5)=x2•sqrt(x)
(4.2) sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(p3) = p • SQRT(p)
Combine both simplifications
sqrt (10p3) =
p • sqrt(10p)
Simplified Root :
p • sqrt(10p)
