Show that ((√ 18 + √ 2)^2)/(√8 - 2) can be written in the form a(b + 2) where a and b are integers.

To approach a question like this we must first simplify the numerator to make things easier. This ends up being equal to 32 (I will demonstrate on the whiteboard). Then we are left with a fraction that has an irrational number as its denominator. Therefore the only way to simplify a fraction like this, and to rearrange it so it is no longer in the form of a fraction, is to rationalize the denominator. We do this by multiplying the fraction by (√8 + 2)/(√8 + 2) since this equals 1 so we’re not changing the fraction but as a result of the rule (a + b)(a - b)=a^2 - b^2 the denominator gets rationalized (will demonstrate on whiteboard). After that it is a case of simplification and you are left with the answer 16(√2 + 1).