Nice Square Root Simplification | Math Olympiad

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[@johnmaulkin-ur8lm]

Another excellent tutorial, thank you. Best regards.

[@MasterTMathsClass]

You are welcome!
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[@-wx-78-]

Once we get to √(64+16√15), nested radical formula gives the result almost immediately:
a = 64 = 2⁶
b = 16²·15 = 2⁸·(2⁴−1) = 2¹²−2⁸
d =√(a²−b) = √[2¹²−(2¹²−2⁸)] = √(2⁸) = 2⁴ = 16
√(64+16√15) = √(a+√b) = √[½(a+d)]+√[½(a−d)] = √[½(64+16)]+√[½(64−16)] = √40+√24.

[@PhilCoolMath]

Great job

[@MasterTMathsClass]

Thanks 🎉