prove that √21 is irrational
Answers
Step-by-step explanation:
The
√
21
. when evaluated produces a number that has a non terminating and non repeating decimal part. Numbers that are rational can all be written in the form:
a
b
b
≠
0
Where
a
and
b
are integers.
Non terminating decimal number that have repeating digits can be written in this form so are called rational numbers.
Examples:
0.3
¯
3
can be written
1
3
0.78
¯¯¯¯
78
can be written
26
33
5
can be written
5
1
and so on.
Because the
√
21
and many many other square roots produce non repeating digits we can't represent them in this way.
This is the square root of 21 to 49 .d.p. as you can see there is no repeating pattern of digits. 4.5825756949558400065880471937280084889844565767680
The proof that values like this can't be written as
a
b
was found by the Greek mathematician Pythagoras, and can be found in text books or online.
Answer:
ab
da
ba
bdjbb
Gb 3 2q
jnnn
a