Find the square root of:

(5) 10404

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Solution

Prime factorisation of 10404:

$\begin{matrix} 2 & 10404 \\ 2 & 5202 \\ 3 & 2601 \\ 3 & 867 \\ 17 & 289 \\ 17 & 17 \\ 1 \end{matrix}$

= 2 × 2 × 3 × 3 × 17 × 17
= (2 × 3 × 17)²

∴ Square root of 10404 = 2 × 3 × 17 = 102

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