The first one you got is correct! Trick to simplifying squares is finding perfect squares hidden in there!
You also got the second one right! Good job! If I worked the example you gave me backwards (7 sqrt.11) then I would have to square 7 to get it back to what it would've been (49) and then multiply that number by 11. Thus, we would've gotten sqrt. 49 x sqrt 11 = sqrt 539. So, if you wanted to simplify the sqrt. of 539, you would pull the sqrt. of 49 and the sqrt. of 11 out of it, and then simplify the sqrt. of 49 to 7 and be left with 7sqrt11. See what I'm saying? If not, let me know.
Sqrt of 48x 2 can be a bit tricky at first glance, but it is deceptively easy. Think about it. What is the square root of x 2? It's just x! The sqrt. of 48 can be reduced to 4sqrt3 because the sqrt16(sqrt3)=sqrt48 (notice how I plucked the perfect square of 16 out of there?) So, your answer would end up as: 4sqrt3x.
You wouldn't want to include a cubed number in the answer of your simplified sqrt, so the answer for the last one you got is incorrect. What you want to do is look for perfect squares in 96. 16 happens to be one! The sqrt16 x sqrt6 = sqrt96. Simplifying the perfect square, we get 4sqrt.6 for our answer.
Hope that helps! As always, if there is anything still not clear, please feel free to repost your problem, and I'll do my best to help you.
Good luck!
Warm Regards,
Grammar Fascist
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