Question 470216
Allen, the main purpose of these problems - remove the root from the denominator
A) {{{4/root(3, 25x^2)}}}
Mulitply numerator and denominator by {{{root(3, 5x)}}}
{{{4/root(3, 25x^2)=(4root(3, 5x))/(root(3, 25x^2)root(3, 5x))=(4root(3, 5x))/(root(3, (5x)^3))=(4root(3, 5x))/(5x)}}}
B) {{{(sqrt(5)-sqrt(6))/(sqrt(5)+sqrt(6))}}}
Mulitply numerator and denominator by {{{(sqrt(5)-sqrt(6))}}}
{{{((sqrt(5)-sqrt(6))(sqrt(5)-sqrt(6)))/((sqrt(5)+sqrt(6))(sqrt(5)-sqrt(6)))=(sqrt(5)-sqrt(6))^2/((sqrt(5))^2-(sqrt(6))^2)=((sqrt(5))^2-2sqrt(5)sqrt(6)+(sqrt(6))^2)/(5-6)=(5-2sqrt(30)+6)/(-1)=-11+2sqrt(30)}}}