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

(a) Let us assume that where a is rational.
Then, squaring both sides-  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.

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