Question

Arătaţi că următoarele numere sunt pătrate perfecte: a 25^37; b4^75, e 121^121; f(2.8)^17; c625^7; g32^19 : 2^19; d 9^27; h 81^125​

Answer 1

Răspuns:

Ai răspuns atașat pe foaie.

Answer 2

Explicație pas cu pas:

$\bf a) \: 25^{37} = \big(5^{2} \big )^{37} = \blue{\big(5^{37} \big )^{2}\rightarrow patrat \: perfect}$

$\bf b) \: 4^{75} = \big(2^{2} \big )^{75} = \green{\big(2^{75} \big )^{2}\rightarrow patrat \: perfect}$

$\bf c) \: 625^{7} = \big(25^{2} \big )^{7} = \orange{\big(25^{7} \big )^{2}\rightarrow patrat \: perfect}$

$\bf d) \: 9^{27} = \big(3^{2} \big )^{27} = \red{\big(3^{27} \big )^{2}\rightarrow patrat \: perfect}$

$\bf e) \: 121^{121} = \big(11^{2} \big )^{121} = \purple{\big(11^{121} \big )^{2}\rightarrow patrat \: perfect}$

$\bf f) \: \big(2 \cdot8 \big)^{17} = \big(4^{2} \big )^{17} = \pink{\big(4^{17} \big )^{2}\rightarrow patrat \: perfect}$

$\bf g) \: 32^{19}:2^{19} =\big(2^{5} \big )^{19} :2^{19}=2^{5\cdot19} :2^{19}=$

$\bf 2^{95 - 19} = 2^{76} = \blue {\big(2^{23} \big )^{2}\rightarrow patrat \: perfect}$

$\bf h) \: 81^{125} = \big(9^{2} \big )^{125} = \green{\big(9^{125} \big )^{2}\rightarrow patrat \: perfect}$