MHB How to Verify a Radical Equation Algebraically?

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To verify a radical equation algebraically, one must isolate the radical on one side and then square both sides to eliminate the radical. After squaring, it is essential to simplify the equation and check for extraneous solutions by substituting back into the original equation. The discussion emphasizes the importance of ensuring both sides of the equation are equal after manipulation. Additionally, referencing previous questions on the topic can provide valuable insights and methods for solving similar problems. This approach ensures a thorough understanding of radical equations and their verification.
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Verify that both sides of the radical equation agree without using a calculator. See picture. How can this be done algebraically?

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You asked this question before:

https://mathhelpboards.com/pre-calculus-21/radical-equation-2-a-23551.html
 
It's good to know that this site keeps a record of posted questions as reference notes.
 
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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