MHB Squaring Radical Within A Radical

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The expression (-2sqrt{8 - 2sqrt{7}})^2 is confirmed to be correctly simplified as 4(8 - 2sqrt{7}). There was initial confusion regarding the notation, specifically the placement of the square root. The discussion clarified that the intended expression involved the square root of 7, not a different notation. Participants agreed on the simplification and confirmed the correct interpretation of the expression. The focus remained on ensuring clarity in mathematical notation and simplification.
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(-2sqrt{8 - 2{7}})^2

(-2sqrt{8 - 2{7}})(-2sqrt{8 - 2{7}})

4(8 - 2sqrt{7})

Correct?
 
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Yes.
 
greg1313 said:
Yes.

Can it be further simplified?
 
Originally you had "(-2sqrt{8 - 2{7}})^2". Where did the sqrt{7} come from? Did you intend to write "(-2sqrt{8 - 2sqrt{7}})^2"?
 
HallsofIvy said:
Originally you had "(-2sqrt{8 - 2{7}})^2". Where did the sqrt{7} come from? Did you intend to write "(-2sqrt{8 - 2sqrt{7}})^2"?

Yes, I intend to write (-2sqrt{8 - 2sqrt{7}})^2.
 

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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