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# Compare Irrational Numbers

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## 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.

1. 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  <

1. 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

1. Which of the two numbers is greater?  or
1. Which of the two numbers is smaller?  or
1. Insert appropriate symbol > or < between the given numbers:
1. Arrange the following numbers in ascending order of their magnitudes:

,  ,

1. Arrange the following numbers in descending order of their magnitudes:

,  ,

1.  < .
2.  <  < .
3.  >  > .

### Arithemetic & Pre Algebra

The Number System

### Algebra

Expressions and Equations

### Statistics and Probability

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