The general reason why it is desirable, is to have a standard form. If for example you look a trig ratios that have radicals, these are given with rationalized denominators, so it makes it easier to recognize these ratios when you rationalize the denominator in your calculations.
The process of rationalizing the denominator is as follows: Multiply both the denominator and numerator by a suitable conjugate that will remove the radicals from the denominator. We need to make sure that all the surds in the given fraction are in their simplified form. If needed, we can simplify the fraction further.
To rationalise the denominator of 1/ (√a + √b), we will follow the given steps: Observe that the denominator has two terms √a + √b We will now multiply the numerator which is 1 in this case and the denominator with the conjugate of the denominator (√a - √b) 1 √a+√b ∗ √a−√b ... By using the algebraic formula, a 2 -b 2 = (a+b) (a-b), we will formulate the above equation as,
We rationalize numerator (vs. denominator) since it removes an apparent singularity at h=0. As a→0, the latter yields the root x=−b/c of bx+c (=ax2+bx+c when a=0). As a→0, the latter yields the root x=−b/c of bx+c (=ax2+bx+c when a=0).
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