Question

Which one of them are irrational : I) 2-√5 ,II) (3+√23)-√23, III) 2√7/7√7! Please help me

Answer 1

I) 2-√5 is an irrational number.
II) (3+√23)-√23=3+√23-√23=3 is not an irrational number.

Answer 2

(I) 2-√5

here 2 is rational but √5 is irrational and difference of rational and irrational number is always irrational. so 2-√5 is irrational

(II) (3+√23)-√23

simplify

= 3 + √23 - √23 = 3

3 is rational so (3+√23)-√23 is rational

(III) 2√7/7√7

simplify = 2√7/7√7 = 2/7 its in the p/q form hence its rational

So only 2-√5 is irrational