Question

How do you simplify `sqrt16/sqrt8`?

Answer 1

=`sqrt2`

Explanation:

`sqrt16/sqrt8` Multiply the fraction by `1` as `sqrt8/sqrt8`:
=`sqrt(16*8)/8` Factor `16` and `8`:
=`sqrt((2*2*2*2))*(2*2*2)` Factor out the three pairs of twos:
=`8sqrt2/8`
=`sqrt2`

OR, if you want to do it the simple way:
`sqrt16/sqrt8`
=`sqrt(16/8)`
=`sqrt2`
Sorry, forgot you could divide them xD ^^

Answer 2

`sqrt2`

Explanation:

Simplify the square roots

`sqrt16/sqrt8` = `4/(sqrt4sqrt2)` = `4/(2sqrt2)`

Rearrange the equation so there is no square root in the denominator

`4/(2sqrt2)` ⋅ `sqrt2/sqrt2` = `(4sqrt2)/(2⋅2)` = `(4sqrt2)/4`

The fours cancel out and you are left with `sqrt2`