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:

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

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

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