How do you order the following from least to greatest #-11/5, -pi, -2.98, -sqrt7#?

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Answer 1 · 2017-02-05T09:57:44

#-pi, -2.98, -sqrt(7), -11/5#

Given:

#-11/5, -pi, -2.98, -sqrt(7)#

Let's get a decimal approximation for #sqrt(7)# first:

Note that #2^2 = 4 < 7 < 9 = 3^2#

So choose #5/2# as a first approximation.

Then applying one step of Newton's method, a better approximation is:

#(5^2+7*2^2)/(2*5*2) = (25+28)/20 = 53/20 = 2.65#

So we have:

#{ (-11/5 = -2.2), (-pi ~~ -3.14), (-2.98 = -2.98), (-sqrt(7) ~~ -2.65) :}#

So in ascending order:

#-pi, -2.98, -sqrt(7), -11/5#