Question #221ff

1 Answer
Feb 23, 2017

Answer:

#sqrt(72a^19)=6abs(a^9)sqrt(2a)#

Explanation:

To find the square root of the given algebraic expression we
#" "#
should find the prime factorization.
#" "#
#72=2xx36#
#72=2xx2xx18#
#72=2xx2xx2xx9#
#72=2xx2xx2xx3xx3#
#72=2^3xx3^2#
#" "#
#72a^19=2^3xx3^2xx(a^9)^2xxa#
#" "#
#sqrt(72a^19)=sqrt(2^3xx3^2xx(a^9)^2xxa)#
#" "#
#sqrt(72a^19)=sqrt(2^2xx2xx3^2xx(a^9)^2xxa)#
#" "#
#sqrt(72a^19)=sqrt((2xx3xxa^9)^2xx2xxa)#
#" "#
#sqrt(72a^19)=abs(2xx3xxa^9)sqrt(2xxa)#
#" "#
#sqrt(72a^19)=6abs(a^9)sqrt(2a)#