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

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

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Answer 1 · 2015-04-13T08:37:24

The Distributive Property of Multiplication tells us that $a \cdot (b + c) = a \cdot b + a \cdot c$ $color(blue)(a*(b + c ) = a*b + a* c$

$2 \sqrt{5} (3 + \sqrt{2})$ $color(red)(2sqrt5(3+sqrt2)$

$= (2 \sqrt{5}) \cdot 3 + (2 \sqrt{5}) \cdot \sqrt{2}$ $= (2sqrt5)*3+(2sqrt5)*sqrt2$

$= 6 \sqrt{5} + 2 (\sqrt{5} \cdot \sqrt{2})$ $= 6sqrt5+2(sqrt5*sqrt2)$

$= 6 \sqrt{5} + 2 (\sqrt{5 \cdot 2})$ $= 6sqrt5+2(sqrt(5*2))$ (Because $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ $color(blue)(sqrta*sqrtb = sqrt(a*b)$

$= 6 \sqrt{5} + 2 \sqrt{10}$ $color(green)(= 6sqrt5+2sqrt(10)$

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

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