How do you simplify #sqrt(75/4 )#?
When you need to simplify numerical root, you should look for these two key facts:
#sqrt(a^2) = a# #sqrt(ab)=sqrt(a)sqrt(b)#
So, anytime you have a number inside a root, you should try to write it as a product of other numbers, of which at least one is a perfect square. Let's analyze your case.
First of all, using the second property, we can write
In fact, every fraction can be read as multiplication using
Now let's deal with the two roots separately: I'd start with the denominator, since we already have a perfect square under a square root, so they simplify (see first rule above): we have
Which leads to the final answer
But how do we find the most appropriate way to rewrite our number, in this case
and select only the primes with even exponent. In this case,
If you are stuck it is always worth have in a 'play' with numbers and see what comes up.
Consider the 75. This is exactly divisible by 5 so
Thus we have:
But 15 is the same as