How do you simplify $(3 \sqrt{6} + 2 \sqrt{10}) (2 \sqrt{2} + 3 \sqrt{5})$ $(3sqrt6 + 2sqrt10) (2sqrt2 + 3sqrt5)$ ?

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How do you simplify $(3 \sqrt{6} + 2 \sqrt{10}) (2 \sqrt{2} + 3 \sqrt{5})$ $(3sqrt6 + 2sqrt10) (2sqrt2 + 3sqrt5)$ ?

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Answer 1 · 2017-07-17T14:30:05

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$(3 \sqrt{6} + 2 \sqrt{10}) (2 \sqrt{2} + 3 \sqrt{5})$ $(color(red)(3sqrt(6)) + color(red)(2sqrt(10)))(color(blue)(2sqrt(2)) + color(blue)(3sqrt(5)))$ becomes:

$(3 \sqrt{6} \times 2 \sqrt{2}) + (3 \sqrt{6} \times 3 \sqrt{5}) + (2 \sqrt{10} \times 2 \sqrt{2}) + (2 \sqrt{10} \times 3 \sqrt{5})$ $(color(red)(3sqrt(6)) xx color(blue)(2sqrt(2))) + (color(red)(3sqrt(6)) xx color(blue)(3sqrt(5))) + (color(red)(2sqrt(10)) xx color(blue)(2sqrt(2))) + (color(red)(2sqrt(10)) xx color(blue)(3sqrt(5)))$

$(6 \sqrt{6} \sqrt{2}) + (9 \sqrt{6} \sqrt{5}) + (4 \sqrt{10} \sqrt{2}) + (6 \sqrt{10} \sqrt{5})$ $(6color(red)(sqrt(6))color(blue)(sqrt(2))) + (9color(red)(sqrt(6))color(blue)(sqrt(5))) + (4color(red)(sqrt(10))color(blue)(sqrt(2))) + (6color(red)(sqrt(10))color(blue)(sqrt(5)))$

We can next use this rule for radicals to simplify the radical terms:

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

$(6 \sqrt{6 \cdot 2}) + (9 \sqrt{6 \cdot 5}) + (4 \sqrt{10 \cdot 2}) + (6 \sqrt{10 \cdot 5})$ $(6sqrt(color(red)(6) * color(blue)(2))) + (9sqrt(color(red)(6) * color(blue)(5))) + (4sqrt(color(red)(10) * color(blue)(2))) + (6sqrt(color(red)(10) * color(blue)(5)))$

$6 \sqrt{12} + 9 \sqrt{30} + 4 \sqrt{20} + 6 \sqrt{50}$ $6sqrt(12) + 9sqrt(30) + 4sqrt(20) + 6sqrt(50)$

We can now rewrite the terms in the radicals and use the above rule in reverse to further simplify the terms:

$6 \sqrt{4 \cdot 3} + 9 \sqrt{30} + 4 \sqrt{4 \cdot 5} + 6 \sqrt{25 \cdot 2}$ $6sqrt(4 * 3) + 9sqrt(30) + 4sqrt(4 * 5) + 6sqrt(25 * 2)$

$(6 \sqrt{4} \sqrt{3}) + 9 \sqrt{30} + (4 \sqrt{4} \sqrt{5}) + (6 \sqrt{25} \sqrt{2})$ $(6sqrt(4)sqrt(3)) + 9sqrt(30) + (4sqrt(4)sqrt(5)) + (6sqrt(25)sqrt(2))$

$(6 \cdot 2 \sqrt{3}) + 9 \sqrt{30} + (4 \cdot 2 \sqrt{5}) + (6 \cdot 5 \sqrt{2})$ $(6 * 2sqrt(3)) + 9sqrt(30) + (4 * 2sqrt(5)) + (6 * 5sqrt(2))$

$12 \sqrt{3} + 9 \sqrt{30} + 8 \sqrt{5} + 30 \sqrt{2}$ $12sqrt(3) + 9sqrt(30) + 8sqrt(5) + 30sqrt(2)$

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How do you simplify $(3 \sqrt{6} + 2 \sqrt{10}) (2 \sqrt{2} + 3 \sqrt{5})$ $(3sqrt6 + 2sqrt10) (2sqrt2 + 3sqrt5)$ ?

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How do you simplify (3√6+2√10)(2√2+3√5)(3sqrt6 + 2sqrt10) (2sqrt2 + 3sqrt5)?

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Explanation:

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How do you simplify $(3 \sqrt{6} + 2 \sqrt{10}) (2 \sqrt{2} + 3 \sqrt{5})$ $(3sqrt6 + 2sqrt10) (2sqrt2 + 3sqrt5)$ ?