a)
[tex]1^{2} +2^{2} =a^{2} \\a^{2} =1+4\\a=\sqrt{5}[/tex]
[tex]2^{2}+a^{2}=b^{2}\\2^{2} +(\sqrt{5})^{2} =b^{2} \\b^{2} =4+5\\b=\sqrt{9} =3[/tex]
[tex]3^{2}+b^{2}=z^{2}\\3^{2} +3^{2}=z^{2} \\z^{2} =9+9\\z=\sqrt{18} =3\sqrt{2}[/tex]
b)
[tex]5^{2} +c^{2} =7^{2}\\25+c^{2} =49\\c^{2} =49-25\\c=\sqrt{24} =2\sqrt{12}[/tex]
[tex]3^{2} +d^{2} =c^{2} \\3^{2}+d^{2}=(2\sqrt{6})^{2} \\9+d^{2} =24\\d^{2} =24-9\\d=\sqrt{15}[/tex]
[tex]d^{2} +4^{2} =z^{2} \\ (\sqrt{15} )^{2}+4^{2} =z^{2} \\z^{2} =15+16\\z=\sqrt{31}[/tex]
