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Sum of Product of Binomial Coefficients

Without actua...

Question

Without actual calculations find the value m of the following expression
$2^{2} + 3^{2} + 6^{2} = m^{2}$

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Solution

$2^{2} + 3^{2} + 6^{2} = m^{2} \Rightarrow 4 + 9 + 36 = m^{2} \Rightarrow 49 = m^{2} \Rightarrow m = 7$

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