1. (3-sqrt6)/(5-2sqrt6)
2. (2sqrt3-sqrt6)/(5sqrt3+2sqrt6)
Don't you do something with the conjugate or something like that?
3-sqrt6 5+2sqrt6
--------- x --------
5-2sqrt6 5+2sqrt6
yes, exactly. Multiply out the numerator, and in the demoninator you will have 25-24 or 1. Nice.
thanks!!
You're welcome! I'm glad I could help.
To simplify the expressions you gave (1. (3-sqrt6)/(5-2sqrt6) and 2. (2sqrt3-sqrt6)/(5sqrt3+2sqrt6)), you can indeed use the conjugate of the denominator. The conjugate of the denominator is found by changing the sign between the two terms, so in the first expression it is 5+2sqrt6, and in the second expression it is 5sqrt3-2sqrt6.
To simplify the expressions using the conjugate, you multiply both the numerator and the denominator by the conjugate. This helps to eliminate the square root from the denominator.
For the first expression:
(3-sqrt6)/(5-2sqrt6) * (5+2sqrt6)/(5+2sqrt6)
To simplify the denominator, you multiply (5-2sqrt6) with (5+2sqrt6), which gives 25-24 or 1.
So, the simplified form of the first expression is 3-sqrt6.
For the second expression:
(2sqrt3-sqrt6)/(5sqrt3+2sqrt6) * (5sqrt3-2sqrt6)/(5sqrt3-2sqrt6)
Again, by multiplying the denominator with its conjugate, the denominator simplifies to 25-24 or 1.
So, the simplified form of the second expression is 2sqrt3-sqrt6.
I hope that clarifies the process of simplifying these expressions using the conjugate! Let me know if you have any more questions.