Question

Find a rational number that is between 5.2 and 5.5. Explain why it is rational.

Answer 1

Rational numbers can be written in form a/b where b≠0

5.2 and 5.5
52/10 and 55/10
so some rational numbers could be
53/10, 54/10


irrational numbers
hmm, most likely the square root numbers
ok, square them
5.2^2=27.04
5.5^2=30.25


5.2<?<5.5
square everybody
27.04<?²<30.25
so pick a number between 27.04 and 30.25
29 or 30 are 2 numbes
I'll pick 29
?²= 29
square root
?=√29
the irrtaional number can be √29
it is 5.39 to the hundreth

Answer 2

Recall what rational numbers are and conversely, what irrational numbers are.
Rational numbers are defined as numbers which can written in fractional notation \frac{a}{b}, where a and b do not have a common factor.

Conversely, irrational numbers cannot be rewritten in fractional form.

As such, an example of a rational number in the interval [5.2, 5.5] is 5.4 because it can be rewritten as \frac{54}{10} = \frac{27}{5}

And an irrational number between the interval can be \sqrt{30}, which comes out to be approximately 5.47723...