How do you simplify #sqrt5(sqrt2+4sqrt2)#?

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Answer 1 · 2017-08-22T12:45:58

See a solution process below:

First, we can factor a #sqrt(2)# out of each term in the parenthesis:

#sqrt(5)(sqrt(2) + 4sqrt(2)) =>#

#sqrt(5)sqrt(2)(1 + 4) =>#

#sqrt(5)sqrt(2)(5) =>#

#5sqrt(5)sqrt(2)#

We can now use this rule for radicals to simplify the radicals:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#

#5sqrt(5 * 2)#

#5sqrt(10)#