Hi, i am having a little trouble understanding the maths in this question

Q83. if two particles retain their charge (q), by what distance must they now be separated in order for the force between to increase by 2?

Worked Solution : Discuss this question

Using Coulomb's equation : F = kq1q2/r2

At original distance, f = kq1q2/r2

r = √(kq1q2/f)

At new distance x, 2f = kq1q2/x2

x = √(kq1q2/2f)

x = (1/√2) x √(kq1q2/f) = (1/√2) x r = r/√2

i understand up to x = 1/√2

im assuming k was given the value of 1 and q1 and q2 are left out because theyre constant, so that

x = √(kq1q2/2f)

But then why is the 1/√2 then multipled by √(kq1q2/f) ??

and then the final value is 1/√2 or r/√2 but doenst this mean the answer would be 0.7?

1/√2 = 0.7 and √1/2 = 0.7 so why is the answer for distance (x or r) then just √2 on its own?

Thanks in advance!