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How do you simplify this expression?3 square root 81 ÷ 5 square root 729

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blahblah523 | Student, Grade 10 | (Level 1) eNoter

Posted November 9, 2012 at 4:55 AM via web

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How do you simplify this expression?

3 square root 81 ÷ 5 square root 729

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted November 9, 2012 at 6:05 AM (Answer #1)

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You need to simplify the following expression such that:

`(3sqrt(81))/(5sqrt729)`

You need to convert the square root into a power such that:

`sqrt 81 = 81^(1/2)`

You should find the prime factors of 81 such that:

`81 = 1*3^4`

Substituting `3^4`  for 81 yields:

`sqrt 81 = (3^4)^(1/2)`

You need to use the property of exponential and multiply the powers such that:

`(a^b)^c = a^(b*c)`

Reasoning by analogy yields:

`(3^4)^(1/2) = 3^(4*(1/2)) = 3^(4/2) => sqrt81 = 3^2 = 9`

You need to convert `sqrt729`  into a power such that:

`sqrt(729) = 729^(1/2)`

You should find the prime factors of 729 such that:

`729 = 3^6 => 729^(1/2) = (3^6)^(1/2) => 729^(1/2) = 3^(6/2) => 729^(1/2) = 3^3`

Hence, substituting 9 for `sqrt 81`  and 27 for `sqrt 729`  in the given expression yields:

`(3sqrt(81))/(5sqrt729) = (3*9)/(5*27) => (3sqrt(81))/(5sqrt729) = 27/(5*27) = 1/5`

Hence, performing the simplification yields `(3sqrt(81))/(5sqrt729) = 1/5.`

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ntretheway | (Level 2) Adjunct Educator

Posted November 9, 2012 at 6:21 AM (Answer #2)

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   (3*sqrt(81)) / (5 *sqrt(729))

square root 81 =  square root (9 * 9) = 9 

square 729 - 27 * 27

thus, we have the following:

(3 * 9) / (5 * 27)

27 = 3 * 9

so now we have

(3 * 9) / (5 * 3 * 9)

the 3 and 9 in the numerator cancel the 3 and 9 in the denominator.

and the simplified result is:

1/5  answer

 

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