What is the square root of 10 times the square root of 20?

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What is the square root of 10 times the square root of 20?

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Answer 1 · 2015-09-09T00:11:09

$10 \sqrt{2}$ $10sqrt(2)$

Explanation:

You need to multiply $\sqrt{10}$ $sqrt(10)$ and $\sqrt{20}$ $sqrt(20)$ .

Before doing that, take a look at $\sqrt{20}$ $sqrt(20)$ . Notice that you can write it as

$\sqrt{20} = \sqrt{2 \cdot 10}$ $sqrt(20) = sqrt(2 * 10)$

If you use the product property of radicals, which tells you that

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

you can write

$\sqrt{2 \cdot 10} = \sqrt{2} \cdot \sqrt{10}$ $sqrt(2 * 10) = sqrt(2) * sqrt(10)$ .

Your expression will now be

$\sqrt{10} \cdot \sqrt{2} \cdot \sqrt{10} = \sqrt{2} \cdot \sqrt{10} \cdot \sqrt{10}$ $sqrt(10) * sqrt(2) * sqrt(10) = sqrt(2) * sqrt(10) * sqrt(10)$

$= \sqrt{2} \cdot \sqrt{10 \cdot 10} = \sqrt{2} \cdot \sqrt{100}$ $=sqrt(2) * sqrt(10 * 10) = sqrt(2) * sqrt(100)$

$= \sqrt{2} \cdot 10 = 10 \sqrt{2}$ $= sqrt(2) * 10 = color(green)(10sqrt(2))$

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What is the square root of 10 times the square root of 20?

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