SOLUTION: Simplify {{{sqrt(12*x^3/5)}}}

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Question 90667: Simplify sqrt%2812%2Ax%5E3%2F5%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2812%2Ax%5E3%2F5%29


sqrt%2812%2Ax%5E3%29%2Fsqrt%285%29 Break up the square roots using the identity sqrt%28x%2Fy%29=sqrt%28x%29%2Fsqrt%28y%29

Now lets simplify the numerator


sqrt%2812%2Ax%5E3%29Start with the given expression
sqrt%284%2A3%2Ax%5E3%29 Factor 12 into 4%2A3

sqrt%284%2A3%2Ax%2Ax%5E2%29 Factor x%5E3 into x%2Ax%5E2

sqrt%284%29%2Asqrt%283%29%2Asqrt%28x%29%2Asqrt%28x%5E2%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

2%2Asqrt%283%29%2Asqrt%28x%29%2Asqrt%28x%5E2%29 Take the square root of the perfect square 4 to get 2

2%2Asqrt%283%29%2Asqrt%28x%29%2Ax Take the square root of the perfect square x%5E2 to get x

2%2Asqrt%283%29%2Ax%2Asqrt%28x%29 Multiply the common terms
2%2Ax%2Asqrt%28x%29%2Asqrt%283%29 Rearrange the terms
2%2Ax%2Asqrt%283x%29 Group the square root terms



So sqrt%2812%2Ax%5E3%2F5%29 becomes 2%2Ax%2Asqrt%283x%29%2Fsqrt%285%29


Now to rationalize the denominator, multiply the expression by sqrt%285%29%2Fsqrt%285%29


%282%2Ax%2Asqrt%283x%29%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29

2%2Ax%2Asqrt%2815x%29%2Fsqrt%2825%29 Multiply

2%2Ax%2Asqrt%2815x%29%2F5 Take the square root of 25 to get 5



So sqrt%2812%2Ax%5E3%2F5%29 simplifies to 2%2Ax%2Asqrt%2815x%29%2F5