We use the Pythagorean Theorem to answer this:
a²+b²=c²
In our case,
[tex](\sqrt{7})^2+b^2=(\sqrt{19})^2[/tex]
[tex]7+b^2=19[/tex]
Subtract 7 from each side:
[tex]7+b^2-7=19-7
\\b^2=12[/tex]
Take the square root of both sides:
[tex]\sqrt{b^2}=\sqrt{12}=\sqrt{4*3}=2\sqrt{3}[/tex]
Although these numbers work in the Pythagorean theorem, they are not Pythagorean triples, as they are not integers.
