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

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**Answer: **

**Step by Step Explanation: **- Let
**a** be a nonzero rational and let √b be irrational.

Then, we have to show that a√b is irrational. - If possible, let a√b be rational number.

Then, a√b = , where x and y are non-zero integers,having no common factor other than 1. - Now, a√b = ⇒ √b = ....(i)
- But, p and aq are both rational and aq ≠0

Therefore, is rational. - 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. - Hence, a√b is irrational.