How to find the rationalising factor of any irrational and rational number ?

Note : Not rationalising denominator but I want ratinalising __factor__

eg : ^{3}√5

^{ 4}√5

^{3}√3

^{3}√5

Prime factorization of 125 = 5 × 5 × 5

So, ^{3}√125 = ^{3}√5 × 5 × 5 = 5

Now, ^{3}√5 × ^{3}√25 = ^{3}√5 × 25 = ^{3}√125 = 5

Thus, when ^{3}√5 is multiplied by ^{3}√25, we obtain the rational number 5.

Therefore, the rationalizing factor of ^{3}√5 is ^{3}√25.

You can find the rationalizing factor of ^{4}√5 and ^{3}√3 using above explained answer.

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