Question 319731
FALSE


Whenever you have a surd of the form (a + root b) as the denominator (a surd is an expression of the form a + root b) it is always easiest to multiply numerator and denominator by (a - root b) since this will make the denominator the difference of two squares and the square of a root eliminates the need to use roots in the denominator.


So,

1/(a + root b) = (a - root b)/((a - root b)(a + root b)) = (a - root b)/(a squared - b)


Therefore
1/(5 + root 3) = (5 - root 3)/((5 - root 3)(5 + root 3)) = (5 - root 3)/(25 - 3) = (5 - root 3)/22


We multiplied numerator and denominator by (5 - root 3)