Solving 72 = 6^2: What is the Technique?

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SUMMARY

The discussion centers on the mathematical technique of simplifying square roots, specifically the expression √72 = 6√2. This simplification involves rewriting the radicand as a product of a perfect square and another integer, allowing for the extraction of the square root of the perfect square. The term 'surds' is used to describe square roots of integers that cannot be simplified to a rational number. The method demonstrated is a fundamental concept in algebra and is essential for understanding more complex mathematical operations.

PREREQUISITES
  • Understanding of square roots and their properties
  • Familiarity with perfect squares
  • Basic algebraic manipulation skills
  • Knowledge of mathematical terminology, specifically 'surds'
NEXT STEPS
  • Study the properties of square roots and their simplification techniques
  • Learn about perfect squares and their identification
  • Explore advanced topics in algebra involving surds
  • Practice simplifying square roots with various examples
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Students, educators, and anyone interested in enhancing their understanding of algebraic concepts, particularly in simplifying square roots and working with surds.

streetmeat
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quick question:

how does this work- (root)72 = 6(root)2

and what is this technique called?
 
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To simplify squareroots one writes the argument as a product, one of which is a square number. So, [itex]\sqrt{72}=\sqrt{36\times 2}=\sqrt{36}\sqrt{2}=6\sqrt{2}[/itex]

The technique I guess would be called simplifying a square root.
 
Square roots of integers are often labelled 'surds' in textbooks.
 

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