Question 66451
You want to go about this the same way you would a normal long division problem. It's hard to do it on the computer but I'll try my best to make it clear for you :)
{{{2y^2-1sqrt(10y^4+3y^2-7)}}}
Now ask yourself, what do I have to multiply {{{2y^2}}}by to get {{{10y^4}}}?
you should come up with {{{5y^2}}}
Now multiply {{{5y^2}}} by the divisor, {{{2y^2-1}}}         
{{{2y^2-1sqrt(10y^4+3y^2-7)-(10y^4-5y^2)}}}
Remember that because you're subtracting the entire quantity the {{{5y^2}}}is added to {{{3y^2}}}, not subtracted.
After simplifying that you should come up with {{{8y^2}}}
bring down the -7 to make {{{8y^2-7}}}
Now ask yourself again, what do I have to multiply {{{2y^2}}} by to get {{{8y^2}}}?
you should come up with 4
multiply 4 by {{{2y^2-1}}} to get {{{8y^2-4}}}
After simplifying that, you will come up with -3
So your answer is {{{5y^2+4 Remainder -3}}}