Given that [image 1] is it ever possible to have [image 2] Explain.

Answer:

Yes, it is possible for 𝑎 + 𝑏 = 𝑎 + 𝑏 a ​ + b ​ = a+b ​ , but only in special cases. This happens if either 𝑎 = 0 a=0 or 𝑏 = 0 b=0, because the square root of 0 is 0. For example, if 𝑎 = 0 a=0, then 0 + 𝑏 = 0 + 𝑏 = 𝑏 = 0 + 𝑏 0 ​ + b ​ =0+ b ​ = b ​ = 0+b ​ . Similarly, if 𝑏 = 0 b=0, the equation also works. In all other cases where both 𝑎 a and 𝑏 b are positive, the sum of the square roots is greater than the square root of the sum.