How do you simplify #sqrt(50a^8)#?

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Answer 1 · 2018-03-18T23:59:10

#5a^4sqrt2#

We can separate the radical into the following:

#color(blue)(sqrt50)*sqrt(a^8)#

We can factor a #sqrt25# out of #sqrt50#. We get:

#color(blue)(sqrt2*sqrt25)*sqrt(a^8)#

Which can be simplified as

#color(blue)(5sqrt2)*color(red)(sqrt(a^8))#

Which can be simplified as

#5sqrt2*color(red)(a^4)#

Thus, we have

#5a^4sqrt2#