How to Compare Irrational Numbers?

Irrational numbers are defined as those numbers which although belong to the real number Set but cannot be represented in the form A /B. But the comparison factor can still be judged in case of Irrational Numbers. Let us see how to compare irrational numbers.

We know that irrational numbers are those which are characterized by the root n √ symbols where the value of 'n' can be any Integer. Solving the irrational numbers is a long procedure. Results that are evaluated for irrational numbers tell that if we have two numbers ⁿ √a and ^m√b where n > m, then value of former one is smaller as compared to the latter, i.e., n √a < m √b. This result is based on the fact that that difference between two numbers “a” and “b” is considerable. For instance, suppose we have two numbers ³ √2 and ⁴ √4, then third root of 2 will be greater than fourth root of the number 4. But same is not the case when difference between “a” and “b” is large. For instance, suppose we have two irrational numbers as ⁴ √16 and ⁵√64. Here the fourth root of 16 is less as compared to 5th root of 64 as ⁴ √16 would equal 2 while ⁵ √64 equals 2√2 and 2√2 > 2.

If the irrational numbers with same powers and different bases are compared, then also circumstances are completely based on the fact i.e. the difference between value of “a” and “b”. For instance, suppose we have the following Rational Numbers: √4, √9, √3 and √16. In these numbers we would observe that if the value of a > b like 9 > 4, then value for a under the root will be greater.