MHB How can a radical equation be verified algebraically without a calculator?

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To verify a radical equation algebraically, isolate the radical on one side and then square both sides to eliminate the radical. After squaring, simplify the resulting equation and solve for the variable. Check the solutions by substituting them back into the original equation to ensure both sides are equal. It's crucial to consider any extraneous solutions that may arise from the squaring process. This method provides a clear approach to verifying radical equations without the need for a calculator.
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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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https://mathhelpboards.com/pre-calculus-21/radical-equation-1-a-23550.html
 
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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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