Compare Irrational Numbers
Compare Irrational Numbers
We have already discussed Rational and Irrational Numbers, so now let us take a look on how to compare irrational numbers.
Irrational numbers include numbers which are not perfect square roots or perfect cube roots and can’t be found out exactly.
For Example ,
,
,
,
,
,
are not perfect square roots.
Similarly ,
,
,
,
,
,
are not perfect cube roots, and hence irrational.
- To compare two irrational numbers which are of the first form , say
and
we find the square of both numbers and compare them
For Example: =
x
= 3,
=
x
= 5 and since 3 < 5 hence
<
.
- To compare two irrational numbers which are of the second form, say
and
we find the cube of both numbers and compare them.
For Example: =
x
x
= 2,
=
x
x
= 3 and since 2 < 3 hence
<
.
For Example Consider and
=
x
x
x
x
= 15,
=
x
x
x
x
= 21 and 15 < 21 hence
<
.
Check Point
- Which of the two numbers is greater?
or
- Which of the two numbers is smaller?
or
- Insert appropriate symbol > or < between the given numbers:
,
- Arrange the following numbers in ascending order of their magnitudes:
,
,
- Arrange the following numbers in descending order of their magnitudes:
,
,
Answer key
<
.
<
<
.
>
>
.
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