Rationalize this expression:

Question

2 on root 3 - by root 2 on 3

Answer 1

To rationalize the given expression, we need to eliminate the radicals from the denominator.

1. Start with the given expression: 2/(√3 - √(2/3))
2. Multiply the numerator and denominator by the conjugate of the denominator, which is (√3 + √(2/3)). This eliminates the radicals from the denominator.
3. Numerator (2) times the conjugate (√3 + √(2/3)) is 2√3 + 2√(2/3).
4. Denominator (√3 - √(2/3)) times the conjugate (√3 + √(2/3)) is (√3)² - (√(2/3))², which simplifies to 3 - 2/3 = 7/3.
5. Therefore, the rationalized expression is (2√3 + 2√(2/3))/(7/3).
6. Simplify further by multiplying the numerator by 3/3 to make the denominator a whole number: (6√3 + 6√(2/3))/7.