# 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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