Rationalize the denominator: 3/(2-rt6)?

Answer 1

Multiply top and bottom by (2 + √6):

3/(2-√6) =
3·(2 + √6) / (2 - √6)·(2 + √6) =
3·(2 + √6) / (2² - √6²) =
3·(2 + √6) / (4 - 6) =
- 3·(2 + √6) / 2 =
(- 6 - 3√6) / 2

Answer 2

3/(2 - sqrt(6))

To rationalize the denominator, multiply top and bottom by the bottom's conjugate, 2 + sqrt(6).

[3(2 + sqrt(6))] / [ (2 - sqrt(6)) (2 + sqrt(6)) ]

Note that, when squaring a square root, you get the argument back. For instance, [sqrt(5)]^2 = 5. Also note that, when multiplying conjugates (a - b)(a + b) together, we get the result (a^2 - b^2). This is precisely how the denominator gets rationalized.

[3(2 + sqrt(6))] / [4 - 6]

Simplify.

[3(2 + sqrt(6))] / (-2)

(-3/2) (2 + sqrt(6))

Answer 3

3 / (2 - √6)

3(2 + √6) / (2 - √6)(2 + √6

6 + 3√6 / 4 - √36

6 + 3√6 / 4 - 6

6 + 3√6 / - 2

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