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Yes.

The square root of a fraction is the square root of the numerator over the square root of the denominator.

First simplify the fraction (making mixed numbers into improper fractions).

Now consider the numerator and denominator separately as whole numbers.

Only perfect squares (the squares of whole numbers) have rational square roots.

If either, or both, of the numerator and denominator is not a perfect square, the square root of the fraction will be irrational

√(11/6) = (√11)/(√6). Neither 11 nor 6 is a perfect square, thus √(11/6) is irrational.

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Q: Is the square root of 11 over 6 an irrational number?
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