She made her mistake at the first step. To simplify a radical, you would find two numbers that multiply by each other to get your original number (under the radical)
and have one of the number be a perfect square.
Her reasoning is wrong because 10*10 is not

. Had she been correct, her answer should have been able to be squared to equal

In other words, she should have done

(We used 25 because 25 is a perfect square, 5*5=25).
:)