SOLUTION: how to solve sqrt(50h^15)

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Question 614606: how to solve sqrt(50h^15)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, only equations or inequalities are solved. What you have is called an expression. Expressions are simplified.

To simplify a square root, you look for perfect square factors of the radicand. ("Radicand" is the name for the expression inside a radical.) SO we look for perfect square factors of 50h%5E15:
sqrt%2850h%5E15%29
sqrt%2825%2Ah%5E2%2Ah%5E2%2Ah%5E2%2Ah%5E2%2Ah%5E2%2Ah%5E2%2Ah%5E2%2A2h%29
Since the radicand is all multiplication, I have used the Commutative Property to rearrange the order of the factors so that all the perfect squares are in front. Note also how I "lumped together" the factors that are not perfect squares, 2h. Neither of these are necessary but I find that it makes the rest of the simplifying a little easier.

Next we use a property of all radicals (including square roots), root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29, to separate all the perfect square factors into their own "personal" square roots:


Now simplify the square roots of the perfect squares:
5%2Ah%2Ah%2Ah%2Ah%2Ah%2Ah%2Ah%2Asqrt%282h%29%29
which simplifies to:
5h%5E7%2Asqrt%282h%29%29
This is your simplified expression.

P.S. The could be done a little faster if you are good with exponents:
sqrt%2850h%5E15%29
sqrt%2825%2A%28h%5E7%29%5E2%2A2h%29
sqrt%2825%29%2Asqrt%28%28h%5E7%29%5E2%29%2Asqrt%282h%29
5h%5E7%2Asqrt%282h%29%29