Write √ 45 in the form a √ 5, where a is an integer.

You can separate any surd into factors of the number that is being square rooted, for example when you have a surd such as √ 12 it can be rewritten as √ 2 X √ 6 or √ 3 X √ 4. This is very useful when we work with surds that have factors that are square numbers, as they can be simplified. Using the example of √ 12 if we separate it into √ 3 X √ 4, we know that 4 is a square number so we can rewrite the √4 as 2. This means we can turn √ 12 into √ 3 X 2 = 2√ 3. When we look at the example in the question we are already given one of the factors, 5. This means if we divide 45 by 5 we will get the other factor, 9. So we have √ 9 X √ 5, we know that 9 is 3 squared so we can just write it as 3√ 5.