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:

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

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