a)
[tex]x^{2} +2^{2} =(\sqrt{24} )^{2} \\x^{2} +4=24 /-4\\x^{2} =20\\x=\sqrt{20} =2\sqrt{5}[/tex]
b)
[tex]x^{2} +5^{2} =7^{2} \\\x^{2} +25=49/-25\\x^{2} =24\\x=\sqrt{24} =2\sqrt{6}[/tex]
c)
[tex]3^{2}+(3\sqrt{7})^{2} =x^{2} \\ x^{2} =9+63\\x^{2} =72\\x=\sqrt{72}=6\sqrt{2}[/tex]
d)
[tex](2\sqrt{3} )^{2} +6^{2} =x^{2} \\x^{2} =12+36\\x^{2} =48\\x=\sqrt{48} =4\sqrt{3}[/tex]
e)
[tex]6^{2} +4^{2} =x^{2} \\x^{2} =36+14\\x^{2} =50\\x=\sqrt{50} =5\sqrt{2}[/tex]
f)
[tex](2\sqrt{5} )^{2} +x^{2} =(2\sqrt{19})^{2} \\20+x^{2} =76 /-20\\x^{2} =56\\x=\sqrt{56} =2\sqrt{14}[/tex]
