How do you reorder this from least to greatest: #\sqrt { 3} ,- \frac { 1} { 3} ,2.1,- \sqrt { 6} ,- 3.5#?

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Answer 1 · 2017-11-06T23:18:28

See a solution process below:

First, we can split these into negative and positive numbers:

#{-1/3, -sqrt(6), -3.5}# and #{sqrt(3), 2.1}#

For the positive numbers, we know #sqrt(4) = 2#

Therefore, #sqrt(3) < 2# so we know #2.1 > sqrt(3)# and we can write the positive numbers, in order from least to greatest as:

#{sqrt(3), 2.1}#

For the negative numbers we know:

#-1/3# is between #-1 and 0#

And we know #sqrt(9) = 3# and #sqrt(4) = 2#

So #=sqrt(6)# must be between #-3# and #-2#

And #-3.5 < 3$

So we can put the negative numbers in order from least to greatest and add to the positive numbers as:

#{-3.5, -sqrt(6), -1/3, sqrt(3), 2.1}#