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Simplify: sqrt -5 times sqrt -15

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted April 23, 2013 at 6:07 PM via web

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Simplify:

sqrt -5 times sqrt -15

3 Answers | Add Yours

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 23, 2013 at 6:17 PM (Answer #1)

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The terms `sqrt(-5)` and `sqrt(-15),` separately, are invalid. Using the properties of multiplication of square roots, yields:

`sqrt(a)*sqrt(b) = sqrt(a*b)`

Reasoning by analogy, yields:

`sqrt(-5)*sqrt(-15) = sqrt((-5)*(-15))`

Performing the multiplication of two negative numbers yields:

`sqrt(-5)*sqrt(-15) = sqrt 75 => sqrt(-5)*sqrt(-15) = 5sqrt 3`

Hence, performing the multiplications `sqrt(-5)*sqrt(-15) = 5sqrt 3.`

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rcmath | High School Teacher | (Level 1) Associate Educator

Posted April 23, 2013 at 7:46 PM (Answer #2)

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`sqrt(-5)*sqrt(-15)=isqrt(5)*isqrt(15)=i^2*sqrt(5*15)=i^2*5sqrt(3)=-1*5sqrt(3)=`

`-5sqrt(3)`

sqrt(-1) only exist in the complex number system. It is defined as the imaginary number i and i^2=-1 not 1.

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Wilson2014 | eNotes Employee

Posted April 25, 2013 at 9:31 PM (Answer #3)

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One thing that was overlooked is that the `sqrt(5*15)` can be plus or minus so the full, complete answer is `+- 5*sqrt (3)` .    

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