Resposta e explicação passo a passo:

[tex]\sqrt{360}\ | \ 2\\ | \ 180 \ | \ 2\\ | \ \ 90 \ \ | \ 2\\| \ \ 45 \ \ | \ 3\\| \ \ 15 \ \ | \ 3\\| \ \ \ 5 \ \ | \ 5\\| \ \ \ 1 \ \ | =\sqrt{2^{2}*2*3^{2}*5} =2*3\sqrt{2*5}=6\sqrt{10}[/tex]

[tex]\sqrt{1521}\ | \ 3\\ | \ \ \ 507 \ | \ 3\\ | \ \ \ 169 \ | \ 13\\| \ \ \ 13 \ \ | \ 13\\| \ \ \ \ 1 \ \ | =\sqrt{3^{2}*13^{2}} =3*13=39[/tex]

[tex]\sqrt{3969}\ | \ 3\\ | \ \ 1323 \ | \ 3\\ | \ \ \ 441 \ | \ 3\\| \ \ \ 147 \ | \ 3\\| \ \ \ \ 49 \ \ | \ 7\\| \ \ \ \ \ 7 \ \ | \ 7\\| \ \ \ \ \ 1 \ \ | =\sqrt{3^{2}*3^{2}*7^{2}} =3*3*7=63[/tex]

[tex]\sqrt{208}\ | \ 2\\ | \ 104 \ | \ 2\\ | \ \ 52 \ \ | \ 2\\| \ \ 26 \ \ | \ 2\\| \ \ 13 \ \ | \ 13\\| \ \ \ 1 \ \ | =\sqrt{2^{2}*2^{2}*13} =2*2\sqrt{13}=4\sqrt{13}[/tex]

[tex]\sqrt{1568}\ | \ 2\\ | \ \ \ 784 \ | \ 2\\ | \ \ \ 392 \ | \ 2\\| \ \ \ 196 \ | \ 2\\| \ \ \ \ 98 \ \ | \ 2\\| \ \ \ \ 49 \ \ | \ 7\\| \ \ \ \ \ 7 \ \ | \ 7\\ | \ \ \ \ \ 1 \ \ | =\sqrt{2^{2}*2^{2}*2*7^{2}} =2*2*7\sqrt{2}=28\sqrt{2}[/tex]