SOLUTION: can you help me simplify this equation? {{{ sqrt( 8a^8 ) }}}

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Question 628206: can you help me simplify this equation? +sqrt%28+8a%5E8+%29+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
(Trivial) Side Note: This is NOT an equation because there is NO equal sign. This is simply an expression.


sqrt%288%2Aa%5E8%29 Start with the given expression.


sqrt%284%2A2%2Aa%5E8%29 Factor 8 into 4%2A2


sqrt%284%2A2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%29 Factor a%5E8 into a%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2


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


2%2Asqrt%282%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29 Take the square root of 4 to get 2.


2%2Asqrt%282%29%2Aa%2Aa%2Aa%2Aa Take the square root of a%5E2 to get a.


2a%5E4%2Asqrt%282%29 Rearrange and multiply the terms.

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Answer:


So sqrt%288%2Aa%5E8%29 simplifies to 2a%5E4%2Asqrt%282%29


In other words, sqrt%288%2Aa%5E8%29=2a%5E4%2Asqrt%282%29 where 'a' is non-negative.

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