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Home » Also, \( 25^2 = 625 \). - Blask

Also, \( 25^2 = 625 \). - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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The sum of the squares of three consecutive integers is 365. What is t...
Let the integers be \( n - 1, n, n + 1 \).
Their squares sum to \( (n - 1)^2 + n^2 + (n + 1)^2 = 365 \).
This expands to \( n^2 - 2n + 1 + n^2 + n^2 + 2n + 1 = 365 \).
Simplifying, \( 3n^2 + 2 = 365 \) leads to \( 3n^2 = 363 \).
Thus, \( n^2 = 121 \), so \( n = 11 \) (since \( n \) is an integer).
A right triangle has legs of lengths 8 and 15. What is the length of t...
Using the Pythagorean theorem, \( a^2 + b^2 = c^2 \), where \( a = 8 \...
Calculating, \( 8^2 + 15^2 = 64 + 225 = 289 \).
Thus, \( c = \sqrt{289} = 17 \).

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