Prove that
(a) is not arational number and
(b) is not arational number.

Using (a  +  b) ² =a ² +  2ab  +  b ²

Now, a is rational is rational and is an irrational number.
Since a rational number cannot be equal to an irrational number. Our assumption that is rational is wrong.

(b) Let us assume that , where p and q are integers, having no common factors and q ≠ 0.

Taking cube both sides—

7q ³ = p ³ ------(i)

⇒ p is a multiple of 7
Thus p is multiple of 7.

Let p = 7m, where m is an integer.
Then, p ³ = 343 m ³ ------(ii)

⇒ 7q ³ = 343 m ³ [from (i) and (ii)]
⇒ q ³ = 49 m ³ ⇒ q ³ is a multiple of 7.
⇒ q is a multiple of 7.

Thus, p and q are both multiples of 7, or 7 is a factor of p and q.
This contradicts our assumption that p and q have no common factors.

Hence is not a rational number.