√5( √8 +√18) can be written in the form a√10 where a is an integer.

First, I would take into account the important parts of the question. I'm looking for an answer in the form of "a√10, where a is an integer". I would explain if not known that an integer is just a whole number.
Then I would address my method for getting to the answer with the shortest amount of work - for example we see that the equation √5( √8 +√18) has a √5 outside the brackets. As we know that √5√2 can be expressed as √10, we know that we need to get √2 from the expression inside the brackets to the outside, factorising it. We then look inside the brackets as to how we can factorise √2. As the expression is √8 +√18 and we know that multiplication and division works the same when the numbers are all a root, we can see that we can factorise this as √2(√4 +√9), which we can further factorise in the context of the question as √2√5(√4 +√9) and simplify as √10(√4 +√9). This gives us a form similar to our required answer. If we solve the terms that are bracketed (√4 +√9) we get ( 2+3) or 5. We can then present the answer in the form 5√10, with a=5.