SOLUTION: Simplify the radical expression. 3 times the (square root of 180h^4)

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Question 179471: Simplify the radical expression.
3 times the (square root of 180h^4)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3%2Asqrt%28180%2Ah%5E4%29 Start with the given expression.


3%2Asqrt%2836%2A5%2Ah%5E4%29 Factor 180 into 36%2A5


3%2Asqrt%2836%2A5%2Ah%5E2%2Ah%5E2%29 Factor h%5E4 into h%5E2%2Ah%5E2


3%2Asqrt%2836%29%2Asqrt%285%29%2Asqrt%28h%5E2%29%2Asqrt%28h%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


3%2A6%2Asqrt%285%29%2Asqrt%28h%5E2%29%2Asqrt%28h%5E2%29 Take the square root of 36 to get 6.


3%2A6%2Asqrt%285%29%2Ah%2Ah Take the square root of h%5E2 to get h.


18h%5E2%2Asqrt%285%29 Rearrange and multiply the terms.

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Answer:


So 3%2Asqrt%28180%2Ah%5E4%29 simplifies to 18h%5E2%2Asqrt%285%29


In other words, 3%2Asqrt%28180%2Ah%5E4%29=18h%5E2%2Asqrt%285%29 where every variable is positive.