Simplify √32+√18 to a*√2 where a is an integer

So firstly, we need to know what type of answer we are aiming for. The question tells us to put our answer in the format a√2 where a is an integer. As we know from previous work, an integer is a whole number, so shouldn't have any fraction or decimal after it. Next we know the answer should be a multiple of √2. To achieve this, we must break down and complete the sum in the question.So, starting with the first term, √32, we know that 32 has multiple factors, 1, 2, 4, 8, 16, and 32. This means we can write 32 as a multiple of two of these numbers, contained within the square root sign, e.g. √(216). Now, once you have written 32 as a multiple of two separate numbers, we can then write it as √2√16. Now, here we have chosen 216 deliberately, as we want to end up with a multiple of √2. We can now simplify this further by noting that √16 = 4, so the √32 can be re-written as 4√2. Doing this again the the √18 we see that it can be rewritten as 3√2. Now we have a sum of multiples of √2. By completing this sum we have now answered the question in the format it asked for.