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Simplify the expression:  `(2sqrt(3)sqrt(36))`  2 square root 3 square root 36

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rawrhappy | Student, Grade 10 | (Level 1) Honors

Posted November 8, 2012 at 2:46 AM via web

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Simplify the expression:  `(2sqrt(3)sqrt(36))`  

2 square root 3 square root 36

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted November 8, 2012 at 4:51 AM (Answer #1)

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`2sqrt(3) sqrt(36)` is not an equation so you can only simplify it. To be an equation, it would have an equal sign (=) and a variable (such as 'x' to solve).

`2sqrt(3) sqrt(36)`      A square root can have a negtive or positive result

= `2sqrt3. 6`  or `2sqrt(3) (-6)`

= `12sqrt(3)` or `-12sqrt(3)`

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mathsworkmusic | (Level 1) Educator

Posted November 8, 2012 at 11:04 AM (Answer #2)

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As user durbanville says, a square root can have a negative or positive result.

So `2sqrt(3)sqrt(36) = 2(-sqrt(3))(-sqrt(36))` or `2(-sqrt(3))(+sqrt(36))` or `2(+sqrt(3))(-sqrt(36))` or `2(+sqrt(3))(+sqrt(36))`

Now `sqrt(36) = sqrt(6^2) = (6^2)^(1/2) = 6^(2(1/2)) = 6`

So `2sqrt(3)sqrt(36) = +2(6)sqrt(3)` or `-2(6)sqrt(3)` or `-2(6)sqrt(3)` or `+2(6)sqrt(3)`

Only two of these are unique so

`2sqrt(3)sqrt(36) = +2(6)sqrt(3)` or `-2(6)sqrt(3)`

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