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 < .
- 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:
- < .
- < < .
- > > .
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