(628)-272-0788 info@etutorworld.com
Select Page

# 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.

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.  >  > .

## eTutorWorld Understands Math Tutoring | Online Math Worksheets are Important Tools

Understanding graphs, charts, and opinion polls in a newspaper, for calculating house and car payments, and for choosing a long-distance telephone service are impossible without strong math skills …and the only way to develop strong math skills is by constant practice.

‘Practice makes a man perfect’ holds true for no other field better than for math. A middle or high school student must set aside a minimum of an hour for math every day. Other than textbooks, worksheets help you revise and understand concepts better.

Our expert tutors prepare online maths worksheets that are age and grade-appropriate. Grade-wise math worksheets for Elementary Math, Arithmetic, Pre-Algebra, Algebra, Geometry, Trigonometry, Statistics, Pre-Calculus and Calculus can be solved to improve math skills, to get ahead or to even catch up.

You may download these FREE online math worksheets in the PDF format, and then print and email us their solutions for a free evaluation and analysis by eTutorworld’smath expert tutors.

You may solve these worksheets by yourself or with your peers while studying together.

The Answer Key at the end of each worksheet allows for a self-evaluation.

## Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12, Test Prep help for Standardized tests like SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a FREE CLASS.

No credit card required, no obligation to purchase.
Just book a free class to meet a tutor and get help on any topic you want!

## Pricing for Online Tutoring

5 sessions1 Month$139 1 session1 Month$28
10 sessions3 months$269 15 sessions3 months$399
20 sessions4 months$499 50 sessions6 months$1189
100 sessions12 months\$2249

### Arithemetic & Pre Algebra

The Number System

### Algebra

Expressions and Equations

## IN THE NEWS

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