How do you simplify the expression $\sqrt{3} (2 + 3 \sqrt{6})$ $sqrt3(2+3sqrt6)$ ?

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Answer 1 · 2017-05-13T13:50:21

See a solution process below:

First, expand the parentheses by multiplying each term within the parentheses by the factor outside the parentheses:

$\sqrt{3} (2 + 3 \sqrt{6}) \Rightarrow$ $color(red)(sqrt(3))(2 + 3sqrt(6)) =>$

$(\sqrt{3} \cdot 2) + (\sqrt{3} \cdot 3 \sqrt{6}) \Rightarrow$ $(color(red)(sqrt(3)) * 2) + (color(red)(sqrt(3)) * 3sqrt(6)) =>$

$2 \sqrt{3} + 3 \sqrt{3} \sqrt{6}$ $2sqrt(3) + 3sqrt(3)sqrt(6)$

We can now use this rule for radicals to simplify the term on the right:

$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ $sqrt(a) * sqrt(b) = sqrt(a * b)$

$2 \sqrt{3} + 3 \sqrt{3} \sqrt{6} \Rightarrow$ $2sqrt(3) + 3sqrt(3)sqrt(6) =>$

$2 \sqrt{3} + 3 \sqrt{3 \cdot 6} \Rightarrow$ $2sqrt(3) + 3sqrt(3 * 6) =>$

$2 \sqrt{3} + 3 \sqrt{18}$ $2sqrt(3) + 3sqrt(18)$

We can use this same rule in reverse to further simplify the term on the right:

$2 \sqrt{3} + 3 \sqrt{18} \Rightarrow$ $2sqrt(3) + 3sqrt(18) =>$

$2 \sqrt{3} + 3 \sqrt{9 \cdot 2} \Rightarrow$ $2sqrt(3) + 3sqrt(9 * 2) =>$

$2 \sqrt{3} + 3 \sqrt{9} \sqrt{2} \Rightarrow$ $2sqrt(3) + 3sqrt(9)sqrt(2) =>$

$2 \sqrt{3} + (3 \cdot 3) \sqrt{2} \Rightarrow$ $2sqrt(3) + (3 * 3)sqrt(2) =>$

$2 \sqrt{3} + 9 \sqrt{2}$ $2sqrt(3) + 9sqrt(2)$

How do you simplify the expression √3(2+3√6)sqrt3(2+3sqrt6)?