Question

How do I solve this using the Pythagorean theorem and leaving it in radical form ?

Answer 1

if the legs of a right triangle are a and b and the hypotnuse is c then
a²+b²=c²

so we are given
the legs are x and √7
and the hypotnuse is √19
so

x²+(√7)²=(√19)²
x²+7=19
minus 7 both sides
x²=12
sqrt both sides
x=√12
x=√(4*3)
x=(√4)(√3)
x=2√3