Question

Stabiliti care dintre urmatoarele numere sunt patrate ale unor numere naturale.
Justificati raspunsul dat.
a) 64, 100, 140, 333, 100000
b) 2⁴, 4²×9, 3⁶,21⁸ ,10⁹, n apartine de numere naturale
${6}^{4 \times n + 1}$

${5}^{2 \times n}$
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Answer 1

$64 = {8}^{2}$

$100 = {10}^{2}$

$140 = 2 \sqrt{35} \: nu \: este \: patrat \: a \: unui \: numar \: natura$

$333 = 3 \sqrt{111} \: nu \: este \: patrat \: a \: unui \: numar \: natural$

$1000000 = {1000}^{2}$

${2}^{4} = 2 \times 2 \times 2 \times 2 = 4 \times 4 = {4}^{2}$

${4}^{2} \times 9 = {4}^{2} \times {3}^{2} = {(4 \times 3)}^{2} = {12}^{2}$

${3}^{6} = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = {3}^{3} \times {3}^{3} = 27 \times 27 = {27}^{2}$

${21}^{8} = {21}^{2} \times {21}^{2} \times \: {21}^{2} \times {21}^{2} = {(21 \times 21 \times 21 \times 21)}^{2}$

${10}^{9} = {10}^{3} \times {10}^{3} \times {10}^{3} = {(10 \times 10 \times 10)| }^{3} \: nu \: este \: patrat \: a \: unui \: numar \: natural$