Question

How do you solve `(8sqrt(6mn) + 6sqrt(8mn))/ (2sqrt(2mn))`?

Answer 1

`4sqrt3 +6`

Explanation:

This is not an equation, but an expression or fraction, so it can be simplified rather than solved,

Write each term in the numerator with its own denominator.

`(8sqrt(6mn))/(2sqrt(2mn) ) + (6sqrt(8mn))/(2sqrt(2mn))`

Note that there is a factor of `sqrt(2mn)` in each part.

Try to isolate it in every part by splitting up the square roots into separate roots.

=`(cancel8^4sqrt(3xx2mn))/(cancel2sqrt(2mn)) +(cancel6^3sqrt(4xx2mn))/(cancel2sqrt(2mn))`

=`(4sqrt3 sqrt(2mn))/(sqrt(2mn)) +(3xx2 sqrt(2mn))/(sqrt(2mn))`

Now we can cancel the factors that are the same:

=`(4sqrt3 cancelsqrt(2mn))/cancel(sqrt(2mn)) +(3xx2 cancelsqrt(2mn))/(cancelsqrt(2mn))`

=`4sqrt3 +6`

Answer 2

`(8sqrt(6mn)+6sqrt(8mn))/(2sqrt(2mn))=4sqrt3+6`

Explanation:

`(8sqrt(6mn)+6sqrt(8mn))/(2sqrt(2mn))`

= `(8sqrt(6mn))/(2sqrt(2mn))+(6sqrt(8mn))/(2sqrt(2mn))`

= `8/2×sqrt((6mn)/(2mn))+6/2×sqrt((8mn)/(2mn))`

= `4sqrt3+3sqrt4=4sqrt3+3×2`

= `4sqrt3+6`