An irrational numberbetween 2 and 3
Answers
Answer:
Irrational numbers are those that never give a clear result. Three of those between
2
and
3
could be:
√
5
,
√
6
,
√
7
, and there are many more that go beyond pre-algebra.
Explanation:
Irrational numbers are always approximations of a value, and each one tends to go on forever. Roots of all numbers that are not perfect squares (NPS) are irrational, as are some useful values like
π
and
e
.
To find the irrational numbers between two numbers like
2
and
3
we need to first find squares of the two numbers which in this case are
2
2
=
4
and
3
2
=
9
.
Now we know that the start and end points of our set of possible solutions are
4
and
9
respectively. We also know that both
4
and
9
are perfect squares because squaring is how we found them.
Then using the definition above, we can say that the root of all NPS numbers between the two squares we just found will be irrational numbers between the original numbers. Between
4
and
9
we have
5
,
6
,
7
,
8
; whose roots are
√
5
,
√
6
,
√
7
,
√
8
.
The roots of these will be irrational numbers between
2
and
3
.
Eg:
√
8
≈
2.82842712474619
where the wavy lines mean approximately, or, we will never have the exact numerical answer.