Express 8/((root3) -1)) in the form a(root3) +b, where a and b are integers.

You would multiply both numerator and denominator by the expression (root3 +1)/(root3 +1). This expression is equal to 1 hence the original expression remains unchanged. The new expression is now (8(root3)+8)/(3-1). We simplify the numerator and denominator to 8((root3)+1)/2. Now we can divide by 2 so we get 4((root3)+1)/1 or 4((root3)+1). Finally we expand the expression to 4(root3)+4. So a=4 and b=4.