Question

rationalise the factor √a+√b

Answer 1

Answer:

Note if a≠ba≠b or at least one of them is not a perfect rational square than a−−√+b√a+b is irrational.

Proof: a rational number has a rational square because rational numbers are closed under multiplication and y2y2 is just y×yy×y.

(a−−√+b√)2=a+b+2×ab−−√(a+b)2=a+b+2×ab

Now abab is only a perfect square if a=ba=b (duh) or a=c2a=c2 and b=d2b=d2 than ab=c2d2=(cd)2ab=c2d2=(cd)2 otherwise ab=c2×kab=c2×k where kk is not a perfect square and ab−−√=c×k−−√ab=c×k. And the root of a non-perfect square is irrational[1]. Also rational times or plus (and so also minus or divided by) irrational is irrational[2][3]. Therefore (a−−√+b√)2(a+b)2 is irrational and subsequently also a

Answer 2

Answer:

If a1/n is the irrational number then its rationalising factor is. ¼½½

;fn a

1/n vifje s; la[;k g S rc bldk ifjes;dj.k xq.kk ad gksxk\

(a) a1-1/n (b) a-1/n (c) a1/n-1 (d)