How do you simplify $\sqrt{3} (2 \sqrt{5} - 3 \sqrt{3})$ $sqrt3(2sqrt5-3sqrt3)$ ?

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Answer 1 · 2017-06-03T18:00:23

Seea solution process below:

First, to eliminate the parenthesis, multiply each term within the parenthesis by the term outside the parenthesis:

$\sqrt{3} (2 \sqrt{5} - 3 \sqrt{3}) \Rightarrow$ $color(red)(sqrt(3))(2sqrt(5) - 3sqrt(3)) =>$

$(\sqrt{3} \cdot 2 \sqrt{5}) - (\sqrt{3} \cdot 3 \sqrt{3}) \Rightarrow$ $(color(red)(sqrt(3)) * 2sqrt(5)) - (color(red)(sqrt(3)) * 3sqrt(3)) =>$

$2 \sqrt{3} \sqrt{5} - 3 \sqrt{3} \sqrt{3}$ $2sqrt(3)sqrt(5) - 3sqrt(3)sqrt(3)$

We can now use this rule for multiplying radicals to simplify the expression:

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

$2 \sqrt{3} \sqrt{5} - 3 \sqrt{3} \sqrt{3} \Rightarrow$ $2sqrt(color(red)(3))sqrt(color(blue)(5)) - 3sqrt(color(red)(3))sqrt(color(blue)(3)) =>$

$2 \sqrt{3 \cdot 5} - 3 \sqrt{3 \cdot 3} \Rightarrow$ $2sqrt(color(red)(3) * color(blue)(5)) - 3sqrt(color(red)(3) * color(blue)(3)) =>$

$2 \sqrt{15} - 3 \sqrt{9} \Rightarrow$ $2sqrt(15) - 3sqrt(9) =>$

$2 \sqrt{15} - (3 \cdot 3) \Rightarrow$ $2sqrt(15) - (3 * 3) =>$

$2 \sqrt{15} - 9$ $2sqrt(15) - 9$

How do you simplify sqrt3(2sqrt5-3sqrt3)√3(2√5−3√3)sqrt3(2sqrt5-3sqrt3)?