60.5k views
4 votes
How can you write the expression with rationalized denominator?
sqrt3 - sqrt6 / sqrt3 + sqrt6

User Hubert OG
by
7.2k points

2 Answers

2 votes

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).

User Crolle
by
8.4k points
4 votes

( 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.


User Gabriel Llorico
by
8.7k points
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