Question

find the unknown side length. simplify answers that are radicals . tell whether the side lengths form a Pythagorean triple

Answer 1

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