document.write( "Question 614606: how to solve sqrt(50h^15) \n" ); document.write( "
Algebra.Com's Answer #386689 by jsmallt9(3758)\"\" \"About 
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.

\n" ); document.write( "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\":
\n" ); document.write( "\"sqrt%2850h%5E15%29\"
\n" ); document.write( "\"sqrt%2825%2Ah%5E2%2Ah%5E2%2Ah%5E2%2Ah%5E2%2Ah%5E2%2Ah%5E2%2Ah%5E2%2A2h%29\"
\n" ); document.write( "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.

\n" ); document.write( "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:
\n" ); document.write( "

\n" ); document.write( "Now simplify the square roots of the perfect squares:
\n" ); document.write( "\"5%2Ah%2Ah%2Ah%2Ah%2Ah%2Ah%2Ah%2Asqrt%282h%29%29\"
\n" ); document.write( "which simplifies to:
\n" ); document.write( "\"5h%5E7%2Asqrt%282h%29%29\"
\n" ); document.write( "This is your simplified expression.

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