# Classify the following numbers as rational or irrational: (i) 2 - √5 (ii) (3 +√23) - √23 (iii) 2√7/7√7

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Classify the following numbers as rational or irrational:

(i) 2 - √5

(ii) (3 +√23) - √23

(iii) 2√7/7√7

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(i) 2 - √5

We kno that √5 = 2.236..., which is an irrational number

2 - √5 = 2 - 2.236..

= -0.236..., which is also an irrational number.

Therefore, we conclude that 2 - √5 is an irrational number.

(ii) (3 +√23) - √23

(3 +√23) - √23 = 3 +√23 - √23 = 3.

Therefore, we conclude that (3 +√23) - √23 is a rational number

(iii)  2√7/7√7

We can cancel √7 n the numerator and denominator, as 7 is the the common number in numerator as well as denominator, to get

2√7/7√7 = 2/7
Therefore, we conclude that 2√7/7√7 is rational number.