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

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Answer 1 · 2015-10-16T09:41:37

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

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

$sqrt(21)*(2+sqrt(21))$

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