Introduction:
The process of rationalizing the denominator involves changing the denominator of a fraction so that it no longer contains a radical. This is done by multiplying the numerator and denominator by a suitable factor that eliminates the radical from the denominator.

Simplifying the Expression:
To rationalize the denominator of the expression root 5 - root 2, we need to find a suitable factor that eliminates the radical from the denominator. The simplest rationalizing factor is the conjugate of the denominator, which is obtained by changing the sign of the radical in the denominator. In this case, the conjugate of root 5 - root 2 is root 5 + root 2.

Applying the Rationalizing Factor:
To apply the simplest rationalizing factor, we multiply both the numerator and denominator of the expression by the conjugate of the denominator, which is root 5 + root 2. This gives us:

(root 5 - root 2) x (root 5 + root 2) / (root 5 - root 2) x (root 5 + root 2)

Simplifying this expression gives us:

(root 5)^2 - (root 2)^2 / (root 5)^2 - (root 2)^2

Which simplifies further to:

5 - 2 / 5 - 2

This gives us a rationalized expression of 3/ (root 5 + root 2).

Conclusion:
The simplest rationalizing factor of root 5 - root 2 is the conjugate of the denominator, which is root 5 + root 2. Multiplying both the numerator and denominator of the expression by this conjugate eliminates the radical from the denominator and gives us a rationalized expression of 3/ (root 5 + root 2).

Root 5 minus root 2
rationalizing factor is
√5+√2
I make it 5-2=3