Question

How to add and subtract radical equations `(3sqrt2)/9 +1/(2sqrt32)+sqrt9/8`?

Answer 1

We first simplify the individual terms as much as possible

`(3sqrt2)/9=sqrt2/3` (divide upper and lower by `3`)

`32=2*16=2*4^2->sqrt32=4sqrt2->`
`1/(2sqrt32)=1/(8sqrt2`

`9=3^2->sqrt9/8=3/8`

Our problem has now evolved into:

`sqrt2/3 + 1/(8sqrt2) +3/8`

We need to take care of the second term by multiplying (above and below) by `sqrt2`

`1/(8sqrt2) *sqrt2/sqrt2=sqrt2/(8*2)=sqrt2/16`

Now we need to get all numerators alike; we'll have to get them to `48` (= smallest common multiple)

`(16*sqrt2)/(16*3) + (3*sqrt2)/(3*16) + (6*3)/(6*8)=`

`(16sqrt2+3sqrt2+18)/48=(19sqrt2+18)/48=19/48sqrt2 +3/8`