How do you simplify $- 4 \sqrt{8} \cdot \sqrt{10}$ $-4sqrt8*sqrt10$ ?

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How do you simplify $- 4 \sqrt{8} \cdot \sqrt{10}$ $-4sqrt8*sqrt10$ ?

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Answer 1 · 2017-07-03T02:47:20

See a solution process below:

Explanation:

First, use this rule for radicals to rewrite the expression:

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

$- 4 \sqrt{8} \cdot \sqrt{10} = - 4 \sqrt{8 \cdot 10} = - 4 \sqrt{80}$ $-4sqrt(color(red)(8)) * sqrt(color(blue)(10)) = -4sqrt(color(red)(8) * color(blue)(10)) = -4sqrt(80)$

Next, rewrite the expression and use the same rule for radicals:

$- 4 \sqrt{80} = - 4 \sqrt{16 \cdot 5} = - 4 \sqrt{16} \cdot \sqrt{5} = (- 4 \cdot 4) \sqrt{5} =$ $-4sqrt(80) = -4sqrt(color(red)(16) * color(blue)(5)) = -4sqrt(color(red)(16)) * sqrt(color(blue)(5)) = (-4 * 4)sqrt(5) =$

$- 16 \sqrt{5}$ $-16sqrt(5)$

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How do you simplify $- 4 \sqrt{8} \cdot \sqrt{10}$ $-4sqrt8*sqrt10$ ?

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