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Between what two consecutive integers do #root3(16)# lie?

Answer 1

Abigail Allen

#2 and 3#

Pressing #root(3)16# into a calculator gives #2,5198#

This decimal value hence lies between the integers #2# and #3#.

That is, #2,3 in ZZ and root(3)16 in [2;3]#

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Answer 2

Abigail Allen

Between #2# and #3#

#2^3 = 8 < 16 < 27 = 3^3#

and #f(x) = x^3# is strictly monotonic increasing, so

#2 = root(3)(2^3) = root(3)(8) < root(3)(16) < root(3)(27) = root(3)(3^3) = 3#

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Answer 3

Julia Adams

√3(16) lies between 4 and 5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.