Question

How do you simplify `sqrt8(5 sqrt 2 - sqrt 18)`?

Answer 1

First, notice that `sqrt8 = sqrt(4*2) = 2sqrt2`

Also, notice that `sqrt18 = sqrt(9*2) = 3sqrt2`

Now we have `2sqrt2(5sqrt2 - 3sqrt2)`

We can just subtract inside the parenthesis

Treating the radicals as variables, just subtract and get `2sqrt2`

Now we have `2sqrt2 * 2sqrt2`

We just multiply the radicals with radicals and integers with integers

`2*2 = 4`
`sqrt2 * sqrt2 = sqrt2^2 = 2`

And finally, just multiply to get `2 * 4 = 8`