[tex]\displaystyle\bf\\9)\\a)\\Metoda~1:\\\sqrt{16\cdot9}=\sqrt{4^2\cdot3^2}=\sqrt{\Big(4\cdot3\Big)^2}=4\cdot3=12\\Metoda~2, cea~din~modelul~de~rezolvare:\\\sqrt{16\cdot9}=\sqrt{2^4\cdot3^2}=\sqrt{\Big(2^2\cdot3\Big)^2}=2^2\cdot3=12\\\\\\b)\\Metoda~1:\\\sqrt{81\cdot625}=\sqrt{9^2\cdot25^2}=\sqrt{\Big(9\cdot25\Big)^2}=9\cdot25=225\\Metoda~2:\\\sqrt{81\cdot625}=\sqrt{3^4\cdot5^4}=\sqrt{\Big(3^2\cdot5^2\Big)^2}=3^2\cdot5^2=225[/tex]
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[tex]\displaystyle\bf\\c)\\\sqrt{5^4\cdot17^{10}}=\sqrt{\Big(5^2\cdot17^5\Big)^2}=5^2\cdot17^5\\\\d)\\\sqrt{2020^2\cdot2^{2020}}=\sqrt{\Big(2020\cdot2^{1010}\Big)^2}=2020\cdot2^{1010}\\\\\\e)\\\sqrt{22^2\cdot3^4\cdot2^6}=\sqrt{\Big(22\cdot3^2\cdot2^3\Big)^2}=22\cdot3^2\cdot2^3=22\cdot9\cdot8=1584\\\\\\f)\\\sqrt{5^6\cdot7^4\cdot10^8}=\sqrt{\Big(5^3\cdot7^2\cdot10^4\Big)^2}=\\\\=5^3\cdot7^2\cdot10^4=125\cdot49\cdot10^4=6125\cdot10^4[/tex]
