In a pseudopythagorean triangle, the sides are all integers and the sum of the square roots of the sides equals the square root of the third side. How many pseudopythagorean triangles are there.

Question

A. none
B. 1
C. 2
D. more than 2

this is such a confusing question

Answer 1

so you want:
√a + √b = √c

just take any two perfect squares, add their square roots and square that to get c

e.g.
a = 1 , b=1, c = 4 ----> √1 + √1 = √4
a = 1 , b = 4, c = 9
a = 4, b = 9, c = 25 ---> √4 + √9 = √25
there will an infinite number of these,

BUT,

remember that they are to form a triangle
and in any triangle, the sum of any two sides must be greater than the 3rd side.
none of the above will work
and it gets worse if a and b get larger
e.g.
a = 25, b = 36, c = 121 , ------ 25+36 < 121 , no such triangle

I conclude that there are no such integer values