Question

How can you write the expression with rationalized denominator?
sqrt3 - sqrt6 / sqrt3 + sqrt6

Answer 1

Answer: The answer is
`-3+(2)/(3)√(18).`

Step-by-step explanation: The given expression is

`E=(\sqrt 3-\sqrt 6)/(\sqrt 3+\sqrt 6).`

we will be rationalising the given expression as follows:

`E\\\\\\=(\sqrt 3-\sqrt 6)/(\sqrt 3+\sqrt 6)\\\\\\=((\sqrt 3-\sqrt 6)^2)/((\sqrt 3+\sqrt 6)(\sqrt 3-\sqrt 6))\\\\\\=\frac{3-2\sqrt {18}+6}{3-6}\\\\\\=(9-2√(18))/(-3)\\\\\\=-3+(2)/(3)√(18).`

Thus, the answer is
`-3+(2)/(3)√(18).`

Answer 2

`( 3-6-2 √(18) )/( -3 ) = -3-6 √(2) /-3=1+2 √(2)`
You amplify with sqrt(3)-sqrt(6).
I hope that this is the answer that you were looking for and it has helped you.