Answer:
i) 2 - √5
The sum or difference between a rational number and an irrational number is always irrational.
Here 2 is a rational number and √5 is an irrational number. Hence 2 - √5 is an irrational number.
ii) (3 + √23) - √23
By simplifying the given expression we get 3.
3 = 3/1, which is in the form of p/q and hence a rational number.
Thus, (3 + √23) - √23 is a rational number.
iii) 2√7 / 7√7
2√7 ÷ 7√7 = 2/7, which is in the form of p/q and hence a rational number.
Thus, 2√7 / 7√7 is a rational number.
iv) 1/√2
1/√2 = (1/√2) × (√2/√2)
= √2/2
= 1.414/2
= 0.702 is a non - terminating, non-recurring decimal which is irrational, and hence 1/√2 is an irrational number.
v) 2π
2π = 2 × 3.1415
π is an irrational number whose value is non-terminating and non-recurring. 2 is a rational number.
The product of a non-zero rational number and an irrational number is always an irrational number.
Hence, 2π is an irrational number.
Step-by-step explanation:
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