exam Maths Puzzle Numerical Ability

Determine if this is rational or irrational:

sqrt 77

This would be rational correct? I know 11 can go in to but it is as well and odd number, so i am not real sure. Thank you for the help!

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exam Other Question

Given -x^2-6x-3, is the vertex a maximum or minimum for the function? What is the value fo that maximum or minimum?

There is nothing in my book about maximums and minimums, please help! If log base 8 of 3=r and log base 8 of 5=s, express log base 8 of 3/64 in terms of r and s.