9514 1404 393
Answer:
0
Step-by-step explanation:
If a=b, you are asking for a whole number c such that ...
c = √(a² +a²) = a√2
If 'a' is a whole number, the only whole numbers that satisfy this equation are ...
c = 0 and a = 0.
0 = 0×√2
The lowest whole number c such that c = √(a²+b²) and a=b=whole number is zero.
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√2 is irrational, so there cannot be two non-zero whole numbers such that c/a=√2.
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<em>Additional comment</em>
If you allow 'a' to be irrational, then you can choose any value of 'c' that you like. Whole numbers begin at 0, so 0 is the lowest possible value of 'c'. If you don't like that one, you can choose c=1, which makes a=(√2)/2 ≈ 0.707, an irrational number. The problem statement here puts no restrictions on the values of 'a' and 'b'.
