SOLUTION: simplify square root of 75a^2 over square root of 5

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Question 87859: simplify square root of 75a^2
over
square root of 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2875%2Aa%5E2%29%2Fsqrt%285%29


Lets simplify the numerator

sqrt%2875%2Aa%5E2%29 Start with the numerator
sqrt%2825%2A3%2Aa%5E2%29 Factor 75 into 25%2A3


sqrt%2825%29%2Asqrt%283%29%2Asqrt%28a%5E2%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

5%2Asqrt%283%29%2Asqrt%28a%5E2%29 Take the square root of the perfect square 25 to get 5

5%2Asqrt%283%29%2Aa Take the square root of the perfect squares and a%5E2 to get a

5%2Asqrt%283%29%2Aa%5E1 Multiply the common terms
5%2Aa%5E1%2Asqrt%283%29 Rearrange the terms
5%2Aa%2Asqrt%283%29 Group the square root terms


So the expression simplifies to

5%2Aa%2Asqrt%283%29%2Fsqrt%285%29

which could also look like this

5%2Aa%2Asqrt%283%2F5%29