OCR, 2016, Higher Maths: Rationalise the denominator 1/(1+sqrt(3))
First make sure they know are clear on what a rational number isAsk them to try multiplying 1 + sqrt(3) by different values to see how to make it a rational numberE.g. they might try (1+sqrt(3))2 ---> see it doesn't work! We still have irrational numbers!Try (1+sqrt(3))(1-sqrt(3)) --> yes!! Middle terms cancel therefore we have a rational number!!Multiply both top and bottom of fraction by factor (1-sqrt(3)) to get answerTalk about theory; for any rationalisation question (a+b)(a-b) = a2+b2so if you see a square root at the bottom but squared number would be rational, use this. We call this the 'conjugate'. https://mrbartonmaths.com/resourcesnew/qotw/Badly%20Answered%20Booklets/badly-answered-1-higher-1.pdf
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