Square root of a rational quantity: Algebra

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Miike012
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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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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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