How do I evaluate something like 3070^2-3069^2?
This looks pretty daunting, but the key to this sort of a problem, which has come up a couple of times in previous PAT tests, is to recognise that this expression is actually the difference of two squares. It can be generalised to the problem of evaluating:
x2-y2
which has as its solution:
x2-y2 = (x+y)(x-y)
so in this case:
30702-30692 = (3070+3069)(3070-3069)=(6139)(1)=6139
SC
Related PAT University answers
All answers ▸How do I approximate an irrational square root without using a calculator?
How are you to find 2007^2 − 2006^2 without a calculator?
Given that during a total solar eclipse the Sun is fully hidden by the Moon, calculate the radius of the Moon. (You may use the following: Solar radius 700,000 km, Sun-Earth distance 150,000,000 km, Moon-Earth distance 400,000 km)
A matchbox of height h and uniform density stands on its end on a table with coefficient of friction μ. For accelerating it horizontally, at acceleration a, whilst upright, at which height y should the acceleration be applied?