How do you find the set in which the real number #-sqrt(0.0625)# belongs?

Answer 1

Hazel Anglin

#-sqrt(0.0625)# is a rational number.

Take note of this:

#0.0625 = 0.125/2 = 0.25/4 = 0.5/8 = 1/16 = (1/4)^2#

Thus:

#sqrt(0.0625) = sqrt((1/4)^2) = 1/4#

Thus:

#-sqrt(0.0625) = -1/4#

This is a rational number, since it is expressible in the form #p/q# for integers #p, q# with #q != 0#. For example: #p=-1# and #q=4#.

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Answer 2

Eva Abramson

The real number -sqrt(0.0625) belongs to the set of negative rational numbers.

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Answer 3

Eli Assouline

The real number -√0.0625 belongs to the set of negative real numbers.

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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.