Understanding Rationalizing Factors
Rationalizing a denominator is an essential technique in algebra to eliminate irrational numbers from the denominator of a fraction. When dealing with expressions involving square roots, such as root 5 - root 2, it is crucial to find a suitable rationalizing factor.
Identifying the Rationalizing Factor
To rationalize the denominator of root 5 - root 2, follow these steps:
- The rationalizing factor for an expression of the form (a - b) is (a + b). Hence, for root 5 - root 2, the rationalizing factor is:
- root 5 + root 2
Rationalization Process
Now, let’s see how the rationalizing factor can be applied:
1. Multiply the expression by its conjugate:
- Multiply both the numerator and denominator by (root 5 + root 2).
2. Simplify the expression:
- The product will yield:
- (root 5 - root 2)(root 5 + root 2) = (root 5)^2 - (root 2)^2 = 5 - 2 = 3.
- The denominator will become rational.
Final Expression
Thus, the rationalized form of 1/(root 5 - root 2) becomes:
- (root 5 + root 2) / 3
This conversion eliminates the irrational number from the denominator, making the expression simpler and easier to work with.
Conclusion
In summary, the simplest rationalizing factor for root 5 - root 2 is root 5 + root 2. This method of rationalization is crucial in algebra for simplifying expressions and solving equations efficiently.

root 5 plus root 2