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I'm in set 1 for maths, and feel like I was the only one this lesson not to understand the work. Usually I understand it.
Anyway, can anyone solve these surds, and provide a method so I know what to do? as there are more questions like this to complete for my homework. Best answer, much appreciated <3
#1)
1
-------
1+√2
#2)
4+√2
--------
3-2√2
(these are fractions, in case its unclear what the dotted line is.)
Roots in the nominator are ugly, nasty and dreadful. Get rid of them whenever possible.
#1
1/(1+√2) | multiply with an ingenious 1
(1/(1+√2))*((1-√2)/(1-√2)) | look at the nominator: (a+b)(a-b)=a²-b²
(1-√2)/(1-2)
(1-√2)/(-1) | be careful not to mess up algebraic signs
-(1-√2)
-1+√2 =0.41421356....
#2
(4+√2)/(3-√2) | same as above: the "ingenious" 1 looks a bit different
((4+√2)/(3-√2))*((3+√2)/(3+√2)) | rearrange for readability
((4+√2)(3+√2))/((3-√2)(3+√2))
(5√2+16)/(9-8)
5√2+16=31.556349....
