How do you simplify #( sqrt32)/ (5 sqrt 14)#?
You have to try and spot common values that can be cancelled out.
Both 32 and 14 are even so 2 has to be a common factor giving:
7 is a prime number so the denominator can not be broken down any further
However, 16 in the numerator can be broken down into
Added extension to solution
I forgot that standard practice is that you try to remove any roots from the denominator!
Multiply by 1 but in the form of
Add this back into the expression.
Rationalize the denominator by multiplying both the numerator and denominator by
Simplify the numerator by multiplying the square roots.
Simplify the square root by factoring.
Simplify the denominator.
Simplify the expression.