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Which statement is true regarding the following: `(sqrt(3)/2)` `(1/sqrt(2))` +...

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foxwit | Student, Undergraduate | (Level 1) Salutatorian

Posted July 25, 2013 at 9:30 PM via web

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Which statement is true regarding the following:

`(sqrt(3)/2)` `(1/sqrt(2))` + `(1/sqrt(2))` `(-1/2)`

a) simplified, it equals: `(sqrt(3)-1)/(2 sqrt(2))`

b) simplified, it equals`(sqrt(3)-1)/(-2 sqrt(2))` ``

c) simplified, it equals `(sqrt(3) +1)/(2 sqrt(2))`

d) none of the above

Note, please disregard the unrationalized `1/sqrt(2)` , just simplify as is.

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ishpiro | Teacher | (Level 3) Associate Educator

Posted August 27, 2013 at 2:32 AM (Answer #2)

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Statement a is true.

Let's simplify the given expression:

`(sqrt(3)/2)*(1/sqrt(2)) +(1/sqrt(2))*(-1/2) = `

`sqrt(3)/(2sqrt(2)) + (-1)/(2sqrt(2)) = (sqrt(3) + (-1))/(2sqrt(2))=`

`=(sqrt(3) - 1)/(2sqrt(2))` , which is the expression in choice a.

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