Square root of a rational quantity: Algebra

Thread starter Miike012
Start date Aug 3, 2011
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Algebra Rational Root Square Square root

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The discussion centers on the confusion surrounding the square root of a rational number, specifically why the square root of a rational quantity, m, can be irrational. It highlights that while m is rational, its square root, sqrt(m), can be a quadratic surd, meaning it may not simplify to a rational number. Participants clarify that sqrt(m) being a ratio of rationals does not guarantee it remains rational. The conversation emphasizes the distinction between rational numbers and their square roots, particularly in cases where m is not a perfect square. Ultimately, the discussion underscores the general rule that the square root of a rational number is not always rational.

Aug 3, 2011

Miike012

Why arnt the two terms eqaul even though the square root of m was solved properly?

And is this a general rule?

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Aug 3, 2011

Dick

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I think by 'quadratic surd' they mean that sqrt(m) is irrational where m is rational. Your last expression shows sqrt(m) is a ratio of rationals. Wouldn't that always be rational?

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