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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. < .
4. < < .
5. > > .

### Arithemetic & Pre Algebra

The Number System

### Algebra

Expressions and Equations

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Site by Little Red Bird Our mission is to provide high quality online tutoring services, using state of the art Internet technology, to school students worldwide.

Connect with us
+1-269-763-4602
+1-269-763-5024

Online test prep and practice
SCAT
CogAT
SSAT
ISEE
PSAT
SAT
ACT
AP Exam

Science Tutoring
Physics Tutoring
Chemistry Tutoring
Biology Tutoring

English Tutoring
Writing
Grammar