Question

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

Answer 1

`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))`