Question

Determinați numărul natural n, ştiind că
$\sqrt{1 } \times \sqrt{2} \times \sqrt{3} \times ...... \times \sqrt{9} \times \sqrt{10} = n \sqrt{7}$
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Answer 1

Explicație pas cu pas:

$\sqrt{1 } \times \sqrt{2} \times \sqrt{3} \times ...... \times \sqrt{9} \times \sqrt{10} = n \sqrt{7}$

$\sqrt{1 \times 2 \times 3 \times ... \times 9 \times 10} = n \sqrt{7}$

$\sqrt{{2}^{8} \times {3}^{4} \times 7 \times {5}^{2} } = n \sqrt{7}$

$n = \sqrt{{2}^{8} \times {3}^{4} \times {5}^{2} }$

$n = {2}^{4} \times {3}^{2} \times 5 \implies n = 720$