Write the rationalize factor of 1/root7-root4

Answer 1

assuming the usual carelessness with parentheses
recall that (a-b)(a+b) = a^2 - b^2
so,
1/(√7-√4) = 1/(√7 - √4) * (√7+√4)/(√7+√4)
= (√7+√4)/(7-4) = (2+√7)/3