Calculus/Surds

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Expert: - 7/17/2009


Question
Please help me to solve these problems

a) 1/1+rt2 + 1/rt2+rt3 + 1/rt3+rt4 + .....99 terms.
b) Simplify 2*rt of(1.5 + rt2)-(1.5+rt2)
c) sq. rt of 12*rt5 + 2*rt55
d) Find 4th power of rt of 1 + rt of 1 + rt of 1
e) Which one of the following is greater
x=rt3-rt2, y=rt6-rt5, z=rt8-rt7

Answer
I can do (a) with a spreadsheet.

I don't see how to do (b) or (c).

On (d), the 4th root of a squareroot cancels to a squareroot.
Note that the rt of 1 at the end is 1.
So the question breaks down to (1+rt(2))^2.
That is 1 + 2rt(2) + 2 = 3 + rt(2).

On (e), the squareroot is increasing and concave down,
so the smaller numbers have a bigger difference.
The answer is x.

Calculus

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