How do you simplify #sqrt(7)*(2 sqrt(3) + 3 sqrt(7))#?

1 Answer
KillerBunny
Oct 16, 2015

#2sqrt(21)+21#, or if you prefer #sqrt(21)*(2+sqrt(21))#.

Explanation:

Expand the multiplications:

#sqrt(7)*(2sqrt(3)+3*sqrt(7)) = 2sqrt(3*7) + 3sqrt(7*7)#

Of course, #sqrt(7*7)=sqrt(49)=7#, so the expression begins

#2sqrt(21)+3*7=2sqrt(21)+21#.

Since #21=sqrt(21)*sqrt(21)#, you can factor #sqrt(21)# and obtain

#sqrt(21)*(2+sqrt(21))#

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