Question

15. On making 646421 soldiers stand in a solid square shape, 5 soldiers are left out, then find how many soldiers are
each row ?
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Answer 1

$Given \: Total \: soldiers = 646421$

/* According to the problem given ,If the soldiers in a solid square shape , 5 soldiers are left */

$Let \: number \: soldiers \: in \:each \:row = x$

$\implies x^{2} = 646421 - 5$

$\implies x^{2} = 646416$

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Resolving 646416 into product of prime factors.

646416 = 2×2×2×2×3×3 ×67×67

= 2⁴ × 3 × 67²

_____________________

$\implies x = \sqrt{ 2^{4} \times 3^{2} \times 67^{2}}$

$\implies x = 2^{2} \times 3 \times 67$

$\implies x = 4 \times 3 \times 67$

$\implies x = 804$

Therefore.,

$\red{ number \: soldiers \: in \:each \:row}$

$\green { = 804 }$

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