Simplifying (sqrt2+sqrt6)/(sqrt2+sqrt3) Is there anything else you can do to reduce it to something "nicer" other than multiplying it by (sqrt3-sqrt2)/(sqrt3-sqrt2) and get sqrt(6)−2+sqrt(18)−sqrt(12)? The reason I think there's a nicer form is because the previous problem in the book was to simplify sqrt(3+2sqrt 2)-sqrt(3-2sqrt 2), which simplifies nicely to sqrt((sqrt 2+1)^2}-sqrt((sqrt 2 - 1)^2) = 2.

Nica2t

Nica2t

Answered question

2022-08-07

Simplifying 2 + 6 2 + 3 ?
Is there anything else you can do to reduce it to something "nicer" other than multiplying it by 3 2 3 2 and get 6 2 + 18 12 ? The reason I think there's a nicer form is because the previous problem in the book was to simplify 3 + 2 2 3 2 2 , which simplifies nicely to ( 2 + 1 ) 2 ( 2 1 ) 2 = 2.

Answer & Explanation

Macie Melton

Macie Melton

Beginner2022-08-08Added 19 answers

You are correct. Multiply by the conjugate which is 2 3
After multiplying by the conjugate we have 2 6 + 12 18 1 which gives 2 + 6 12 + 18 . The only further simplification is as follows: Simplify 12 and 18 and we have 2 + 6 2 3 + 3 2
bsmart36

bsmart36

Beginner2022-08-09Added 2 answers

Well, you could note that
6 2 + 18 12 = 2 + 6 ( 1 2 + 3 )
But beyond that, it doesn't look any better.

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