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

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The discussion focuses on simplifying the square root of 72, demonstrating that √72 can be expressed as 6√2 by factoring 72 into a product of a square number (36) and another integer (2). This technique is known as simplifying a square root. The term 'surds' is used in textbooks to refer to square roots of integers that cannot be simplified further. The process involves breaking down the square root into its constituent parts to make calculations easier. Understanding this technique is essential for working with square roots in mathematics.
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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, \sqrt{72}=\sqrt{36\times 2}=\sqrt{36}\sqrt{2}=6\sqrt{2}

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

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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