Please help! If we write in the form , such that , , and are positive integers and is as small as possible, then what is ?

Step-by-step explanation:

Let’s first simplify our expression. We have:

For the second term, multiply both the numerator and denominator by √2. This yields:

Similarly, for the fourth term, multiply both the numerator and denominator by √3. This yields:

Hence, our expression is now:

Let’s combine them. First, we will need common denominators.

Our denominators are 2 and 3. So, our common denominator will be its LCM.

The LCM of 2 and 3 is 6.

Hence, let’s make each term’s denominator 6.

For the first term, we can multiply both layers by 6. Hence:

For the second term, we can multiply both layers by 3. Hence:

For the third term, we can multiply both layers by 6. Hence:

And for the last term, we can multiply both layers by 2. Hence:

So, our expression is:

Add:

Combine like terms:

This cannot be simplified. So, c is as small as possible.

Hence: a=9, b=8, and c=6.

Therefore:

answer: the four apples you took away.

step-by-step explanation: