SOLUTION: square root 36a^9b^12 / 3ab^7

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Question 189060: square root 36a^9b^12 / 3ab^7
Answer by jim_thompson5910(35256) About Me  (Show Source):
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sqrt%28%2836a%5E9b%5E12%29%2F%283ab%5E7%29%29 Start with the given expression.


sqrt%28%2812a%5E9b%5E12%29%2F%28ab%5E7%29%29 Divide 36 into 3 to get 12


sqrt%2812a%5E%289-1%29b%5E%2812-7%29%29 Divide the variable terms by subtracting the corresponding exponents.


sqrt%2812a%5E8b%5E5%29 Subtract


sqrt%284%2A3%2Aa%5E8%2Ab%5E5%29 Factor 12 into 4%2A3


sqrt%284%2A3%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Ab%5E5%29 Factor a%5E8 into a%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2


sqrt%284%2A3%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Ab%5E2%2Ab%5E2%2Ab%29 Factor b%5E5 into b%5E2%2Ab%5E2%2Ab


Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


Take the square root of 4 to get 2.


2%2Asqrt%283%29%2Aa%2Aa%2Aa%2Aa%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29 Take the square root of a%5E2 to get a.


2%2Asqrt%283%29%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Asqrt%28b%29 Take the square root of b%5E2 to get b.


2a%5E4b%5E2%2Asqrt%283b%29 Rearrange and multiply the terms.

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Answer:


So sqrt%28%2836a%5E9b%5E12%29%2F%283ab%5E7%29%29 simplifies to 2a%5E4b%5E2%2Asqrt%283b%29


In other words, sqrt%28%2836a%5E9b%5E12%29%2F%283ab%5E7%29%29=2a%5E4b%5E2%2Asqrt%283b%29 where a%3E0 and b%3E0