How to do Difficult Surd Algebraic manipulation questions example: Rationalise the denominator of the expression: 1+5^(1/2) / 3+5^(1/2). Give your answer in its simplest form:

The first thing to do, is to assess how far the student has managed to work, and then find the missing pieces within the students skill or knoweldge. I might decide to go through the question with the student straight away or, depending on the difficulty for the student, I would encaurage the student to work on some less-difficult questions that have similar elements from the hard question in them. I would do this in order to get them back up to speed on the key points that they need to remember when handling these type of questions.The qeustion was : Rationalise the denominator of the expression: 1+5^1/2 / 3+5^1/2 . Give your answer in its simplest form:For this question, I would tell the student what one is trying to do. One doesnt want the surd form at the bottom, thus in order to get rid of it, we multiply both the top and the bottom by (3-5^1/2 ). We do this because we know from expanding brackets that following the difference of squares formula (a+b) * (a-b) = a² + b² and this would mean that the surd would disappear at the bottom. (I would write down the steps to make it more clear, plus if I feel it is neccessary I would explain as to why the numbers :(3-5^1/2) )Afte that, one would follow through with the algebra, and try to simplify the fraction down to its simplest form.