Question

Aratati ca urmatoarele numere sunt patrate perfecte:16x25;2^18x3^6;25x3^18;16x100;4^15x121^17;5^14x7^8x13^24;3^25+3^34;2^25-7x2^20.Urgent!!!!!!!!!!1Dau coroana!!!!!!!!1

Answer 1

Răspuns:

16x25=4²·5²=(4·5)²

2^18x3^6=(2⁹)²·(3³)²

25x3^18=5²·(3⁹)²

16x100=4²·10²

4^15x121^17=(2¹⁵)²·(11¹⁷)²

5^14x7^8x13^24=(5⁷)²·(7⁴)²·(13¹²)²

3^25+3^34=3³⁴·(3+1)=(3¹⁷)²·2²

2^25-7x2^20=2²⁰(2⁵-7)=(2¹⁰)²·5²

- orice număr natural care poate fi scris ca o putere cu exponentul par este pătrat perfect

Answer 2

Răspuns:

Dacă pot fi scrise sub formă de a^2, sunt pătrate perfecte.

$16 \times 25 = {2}^{4} \times {5}^{2} = ( {2}^{2} \times 5)^{2} pp$

${2}^{18} \times {3}^{6} = ( {2}^{9} \times {3}^{3} )^{2} pp$

${5}^{2} \times {3}^{18} = ( {3}^{9} \times 5)^{2} pp$

${2}^{4} \times {10}^{2} = ( {2}^{2} \times 10)^{2} pp$

$( {2}^{2} )^{15} = ( {2}^{15} )^{2}$

$( {11}^{2} )^{17} = ( {11}^{17} )^{2} = > inmultirea \: este \: pp$

${5}^{14} \times {7}^{8} \times {13}^{24} = ( {5}^{7} \times {7}^{4} \times {13}^{12} )^{2} pp$

${3}^{25} + {3}^{24} = {3}^{24}(3 + 1) = {3}^{24} \times {2}^{2} = (2 \times {3}^{12} )^{2} pp$

${2}^{25} - 7 \times {2}^{20} = {2}^{20} ( {2}^{5} - 7) = {2}^{20} (32 - 7) = {2}^{20} \times {5}^{2} = ( {2}^{10} \times 5)^{2} pp$