Question

How do you simplify `sqrt200-sqrt32`?

Answer 1

`6sqrt(2)`

Explanation:

`sqrt(2xx10^2)-sqrt(2xx4^2)`

`10sqrt(2)-4sqrt(2)`
'~~~~~~~~~~~~~~~~~~~~~~
compare to `10x-4x=6x`
'~~~~~~~~~~~~~~~~~~~~~~~~~~
`=>6sqrt(2)`

Answer 2

`6sqrt2`

Explanation:

Breaking the values down into the prime factors is always possible, but sometimes a bit tedious and often unnecessary if square numbers are recognised as being factors. 200 = 100 x 2 is an obvious example.

`sqrt200 - sqrt32`
= `sqrt(100xx2) - sqrt(16xx2`
= `10sqrt2 - 4sqrt2`
= `sqrt2(10-4)`
= `6sqrt2`