All Real numbers can be classified as rational and irrational numbers. Irrational numbers are . Irrational numbers are non –terminating non recurring decimals that cannot be expressed as fraction .
List of irrational numbers are as follow :
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| Irrational numbers |
- All non perfect square roots are irrational numbers.Some example of irrational squareroots are √2 , √3 , √5 √7, √11, √13, √17 , √19 , √21…………….etc. as √2=1.4141.4142135623…………………, √3=1.73205 08075 68877………….and so on ….All these squarroots have non-terminating non-recurring decimals which can never be expressed as fractions.so they are irrational.
- Like squareroots many cuberoots are also irrational . 3√ 3 , 3√ 5 , 3√ 7 , 3√ 14 etc
- Some natural constants like ∏=3.14159 26535 89793…………………..and e=2.71828 18284 59045…………………………….., etc are irrationals
- Sum of rational and irrationals are irrational .Let us take an example of 3 + √2 …which is irrational.
- Difference of rational and irrationals are irrational . For example 2 - √5 .. is irrational.
- Product of rational and irrational are irrational.For example 2 √7. are irrational
- Quoitent of rational and irrational numbers are irrational √7/√5 are irrational
- Negative of an irrational number is irrational. - √5 , - √7 , - √11… all are irrational number.
- The product of non-zero rational number and an irrational number is an irrational number. Let us take an example of irrational number . List two irrational number between . √2 and √7.In order to find irrational number we will first square of . √2 and . √7. (. √2) ² = 2 and (√7.) ²= 7 , As 2< 3< 5<7 it follows that √2< √3 < √5 < √7 , therefore √3 and √5 lies between √2 and √7 . Hence two irrational number between √2 and √7 are √3 and √5.
