# How do you simplify #sqrt(75/4 )#?

##### 2 Answers

#### Explanation:

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

As for

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,

#### Explanation:

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