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

Oct 16, 2015

Answer:

$2 \sqrt{21} + 21$, or if you prefer $\sqrt{21} \cdot \left(2 + \sqrt{21}\right)$.

Explanation:

Expand the multiplications:

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

Of course, $\sqrt{7 \cdot 7} = \sqrt{49} = 7$, so the expression begins

$2 \sqrt{21} + 3 \cdot 7 = 2 \sqrt{21} + 21$.

Since $21 = \sqrt{21} \cdot \sqrt{21}$, you can factor $\sqrt{21}$ and obtain

$\sqrt{21} \cdot \left(2 + \sqrt{21}\right)$