process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator.
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No, that is not what you do.
Sometimes the denominator is an irrational or complex number (depending on the level that you are at). Rationalising the denominator requires to multiply both the numerator and denominator of the fraction by a suitable number - usually the conjugate - so that when simplified, the denominator is rational - normally an integer.
If you want to rationalize the denominator, then multiply numerator & denominator by sqrt(5), so 8*sqrt(5)/5 = approx 3.578