How do you simplify #sqrt(98n^19)#?

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Answer 1 · 2016-01-15T13:40:30

#=7 color(blue)(n^(19/2))sqrt(2)#

#sqrt(98n^19)#

Upon prime factorising (simplification):
#98 = 7 xx 7 xx 2#

#sqrt(98n^19)= sqrt(7xx7xx2xx n^19) =sqrt(7^2 xx 2xx n^19) =7sqrt(2xx n^19)#

Further, Square root , can also be called as second root so in terms of fraction:
#sqrt(n^19)=n^(19xx 1/2) = n^color(blue)(19/2#

The expression now becomes:

#7sqrt(2xx n^19) = 7 xx color(blue)(n^(19/2))sqrt(2)#

#=7 color(blue)(n^(19/2))sqrt(2)#