Question

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

Answer 1

The answer is precisely 20.

Explanation:

One of the properties of square roots is

`sqrt a xx sqrt b = sqrt (axxb)`

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

So:

`sqrt 10 xx sqrt 40 = sqrt(10 xx 40)`
`color(white)(sqrt 10 xx sqrt 40) = sqrt(400)`
`color(white)(sqrt 10 xx sqrt 40) = 20`

since `20^2 = 400`.