Question -
Answer -
Q (i) 1/√2
Solutions:
(i) 1/√2
Let us 1/√2 is rational.
Then we can find co-prime x and y (y ≠ 0)
Then1/√2 = x/y
Rearranging, we get,
√2 = y/x
Since, x and y are integers, thus, √2 is arational number, which contradicts the fact that √2 is irrational.
Hence, we can conclude that 1/√2 isirrational.
Q (ii) 7√5
Solutions:
(ii) 7√5
Let us 7√5 is a rational number.
Then we can find co-prime a and b (b ≠ 0)
Then 7√5= x/y
Rearranging, we get,
√5 = x/7y
Since, x and y are integers, thus, √5 is arational number, which contradicts the fact that √5 is irrational.
Hence, we can conclude that 7√5 is irrational.
Q (iii) 6 + √2
Solutions:
(iii) 6+√2
Let us 6 +√2 is a rational number.
Then we can find co-primes x and y (y ≠ 0)
Then 6 +√2 = x/y⋅
Rearranging, we get,
√2 = (x/y) – 6
Since, x and y are integers, thus (x/y) – 6 isa rational number and therefore, √2 is rational. This contradicts the fact that√2 is an irrational number.
Hence, we can conclude that 6 +√2 is irrational.