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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SUMMARY

The discussion centers on the concept of square roots of rational quantities, specifically addressing the confusion surrounding the term "quadratic surd." It is established that while m is a rational number, the square root of m, denoted as sqrt(m), can be irrational if m is not a perfect square. The participants clarify that sqrt(m) being a ratio of rationals does not guarantee that it remains rational, particularly when m is a non-square integer.

PREREQUISITES

Understanding of rational and irrational numbers
Familiarity with square roots and their properties
Basic knowledge of algebraic expressions
Concept of perfect squares in mathematics

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Research the properties of square roots of rational numbers
Study the definition and examples of quadratic surds
Explore the implications of non-perfect squares on rationality
Learn about algebraic expressions involving square roots

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Students of algebra, mathematics educators, and anyone interested in the properties of rational and irrational numbers.

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?