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What is the square root of 10 times the square root of 40?

1 Answer

May 9, 2018

The answer is precisely 20.

Explanation:

One of the properties of square roots is

$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ $sqrt a xx sqrt b = sqrt (axxb)$

as long as $a$ $a$ and $b$ $b$ are non-negative real numbers.

So:

$\sqrt{10} \times \sqrt{40} = \sqrt{10 \times 40}$ $sqrt 10 xx sqrt 40 = sqrt(10 xx 40)$
$\sqrt{10} \times \sqrt{40} = \sqrt{400}$ $color(white)(sqrt 10 xx sqrt 40) = sqrt(400)$
$\sqrt{10} \times \sqrt{40} = 20$ $color(white)(sqrt 10 xx sqrt 40) = 20$

since $20^{2} = 400$ $20^2 = 400$ .

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