( k^2-20k+100 ) is the square of what?

Correct answer: ( (k-10)^2 )

The direct answer is B:
\(k^2-20k+100=(k-10)^2\). Start with the identity \((a-b)^2=a^2-2ab+b^2\). Here, take \(a=k\) and \(b=10\). Then \((k-10)^2=k^2-2(k)(10)+10^2=k^2-20k+100\), exactly the given expression. Therefore its square root expression is \((k-10)\). Option A, \((k+20)^2\), would give \(k^2+40k+400\), so both the middle term and constant are wrong. Option B gives the exact expansion, so it is correct. Option C, \((k+10)^2\), gives \(k^2+20k+100\); the sign of the middle term is wrong. Option D, \((k-100)^2\), gives \(k^2-200k+10000\), which is also different. The important clue is that the last term is \(100=10^2\), and the middle term is negative \(-20k=-2(k)(10)\). Memory trick: a negative middle term usually indicates the form \((a-b)^2\), while a positive middle term indicates \((a+b)^2\). Always expand the proposed square to check it.