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 [tex] \sqrt{50} [/tex]. Had she been correct, her answer should have been able to be squared to equal [tex] \sqrt{50} [/tex]
In other words, she should have done [tex] \sqrt{25*2}= \sqrt{25} * \sqrt{2}=5 \sqrt{2} [/tex]
(We used 25 because 25 is a perfect square, 5*5=25).
:)
