Question

How do you simplify `sqrt52-sqrt1300`?

Answer 1

See a solution process below:

Explanation:

We can rewrite the terms within the radicals as:

`sqrt(4 * 13) - sqrt(4 * 325)`

Using this rule for multiplication of radicals we can rewrite each radical as:

`sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))`

`sqrt(color(red)(4) * color(blue)(13)) - sqrt(color(red)(4) * color(blue)(325)) = (sqrt(color(red)(4)) * sqrt(color(blue)(13))) - (sqrt(color(red)(4)) * sqrt(color(blue)(325))) =`

`sqrt(color(red)(4))(sqrt(color(blue)(13)) - sqrt(color(blue)(325))) = 2(sqrt(13) - sqrt(325)`

We can now simplify the radical on the right as:

`2(sqrt(13) - sqrt(color(red)(25) * color(blue)(13))) = 2(sqrt(13) - (sqrt(color(red)(25)) * sqrt(color(blue)(13)))) =`

`2(sqrt(13) - 5sqrt(color(blue)(13))) = 2sqrt(13)(1 - 5) = 2sqrt(13) * -4 =`

`-8sqrt(13)`

Or

`-28.8` rounded to the nearest 10th