Indices and Surds : Properties of Numbers between 0 and 1
Let’s take a number between 0 and 1 (both numbers excluded) and try to find out the value of its indices and surds.
Let’s take x = 0.1
and try to find its power
We can clearly see that the value of x is continuously decreasing as the power is increasing.
Similarly let’s try to find its surds
![\sqrt[3]{0.1} = 0.464](http://webmaggu.com/wp-content/ql-cache/quicklatex.com-4f64727c70ea22ad8b198626810dcb40_l3.png "Rendered by QuickLaTeX.com")
![\sqrt[4]{0.1} = 0.562](http://webmaggu.com/wp-content/ql-cache/quicklatex.com-3c73e095c9623080389631b28d07ebab_l3.png "Rendered by QuickLaTeX.com")
![\sqrt[5]{0.1} = 0.630](http://webmaggu.com/wp-content/ql-cache/quicklatex.com-6b36df8b4addc81cd9691526b108b789_l3.png "Rendered by QuickLaTeX.com")
We can clearly see that the value of x is continuously increasing as the order of surd is increasing.
So if a number x is such that 0<x<1, then ![....\sqrt[4]{x} > \sqrt[3]{x} > \sqrt{x} > x > x^2 > x^3 > x^4 ..........](http://webmaggu.com/wp-content/ql-cache/quicklatex.com-08cbbfa682917a9a79e49d4793d8fbed_l3.png "Rendered by QuickLaTeX.com")
According to the above property we can easily say that.
