A student is asked to solve b2 + a2 = c2 for a and gives the following solution. Assume all variables represent positive Real Numbers.

Question

b2 + a2 = c2
pb2 + a2 = pc2
b + a = c
a = c-b

Explain the mistake(s) made by the student and provide the correct solution.

Answer 1

p? do you mean √?
√(b^2+a^2) = √c^2
clearly the next step is flawed.

√(b^2+a^2) ≠ b+a

while √(b^2*a^2) = √b^2 * √a^2,
√(b^2+a^2) ≠ √b^2 + √a^2

I figure you can take it from there

Answer 2

a^2+b^2=c^2

a^2=c^2-b^2

a=square root of (c^2-b^2)