### If a is a nonzero rational and √b is irrational number then show that a√b is irrational number.

Step by Step Explanation:
1. Let a be a nonzero rational and let √b be irrational.
Then, we have to show that a√b is irrational.
2. If possible, let a√b be rational number.
Then, a√b =
 x y
, where x and y are non-zero integers,having no common factor other than 1.
3. Now, a√b =
 x y
⇒ √b =
 x ay
....(i)
4. But, p and aq are both rational and aq ≠0
Therefore,
 x ay
is rational.
5. Thus, from (i), it follows that √b is rational number.
Where, this contradict the fact that √b is irrational.
However, this contradiction arises by assuming that a√b is rational.
6. Hence, a√b is irrational.

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