What is the square root of 8 times the square root of 20?

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What is the square root of 8 times the square root of 20?

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Answer 1 · 2018-06-27T12:29:19

See a solution process below:

Explanation:

We can rewrite the expression:

$\sqrt{8} \times \sqrt{20}$ $sqrt(8) xx sqrt(20)$

using the following rule for radicals:

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

$\sqrt{8} \cdot \sqrt{20} \Rightarrow \sqrt{8 \cdot 20} \Rightarrow \sqrt{160}$ $sqrt(color(red)(8)) * sqrt(color(blue)(20)) => sqrt(color(red)(8) * color(blue)(20)) => sqrt(160)$

Now, we can use this rule for radicals to simplify the radical:

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

$\sqrt{160} \Rightarrow \sqrt{16 \cdot 10} \Rightarrow \sqrt{16} \cdot \sqrt{10} \Rightarrow 4 \sqrt{10}$ $sqrt(160) => sqrt(color(red)(16) * color(blue)(10)) => sqrt(color(red)(16)) * sqrt(color(blue)(10)) => 4sqrt(10)$

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What is the square root of 8 times the square root of 20?

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