What is #4sqrt7+8sqrt63#?

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Answer 1 · 2017-05-12T13:22:54

See a solution process below:

First, we can use this rule for radicals to rewrite the term on the right:

#sqrt(a * b) = sqrt(a) * sqrt(b)#

#4sqrt(7) + 8sqrt(63) =>#

#4sqrt(7) + 8sqrt(9 * 7) =>#

#4sqrt(7) + (8sqrt(9) * sqrt(7)) =>#

#4sqrt(7) + (8 * 3 * sqrt(7)) =>#

#4sqrt(7) + 24sqrt(7)#

We can now simplify by factoring #sqrt(7)# from each term and combining like terms:

#(4 + 24)sqrt(7) =>#

#28sqrt(7)#