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√5 – Why leave your working in Surd Form?


A good follow up question to the last post. A really good reason to leave working in surd form (that is, with the root sign rather than the decimal) is to avoid doing calculations. But a much better reason is to do with the nature of irrational numbers – it is much more accurate to NOT round your decimals when you start your calculations as this will affect the final answer. So, engineers (and others) leave pi and other irrationals in their surd form to help make their final calculations accurate. That’s a good reason to learn to use surds when doing high school Algebra!

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The graph on the left (Coronavirus) is for a time period of 30 days, while the one on the right (SARS) is for 8 months! Very poor graphical comparison and hardly relevant, unless it is attempting to downplay the seriousness of the coronavirus?

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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