document.write( "Question 705440: I have a question to simplify the square root of 216. I think the answer is 6 times the square root of 6, but I'm not sure... \r
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Algebra.Com's Answer #434599 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
You are 100% correct\r
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\n" ); document.write( "\n" ); document.write( "For more help/practice with simplifying square roots, check out this solver: http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver\r
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Solved by pluggable solver: Simplifying Square Roots (whole numbers only)
\"sqrt%28216%29\" Start with the given expression
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\n" ); document.write( " The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.
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\n" ); document.write( " So let's list the factors of 216
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\n" ); document.write( " Factors:
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\n" ); document.write( " 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
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\n" ); document.write( " Notice how 36 is the largest perfect square, so lets factor 216 into 36*6
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\n" ); document.write( " \"sqrt%2836%2A6%29\" Factor 216 into 36*6
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\n" ); document.write( " \"sqrt%2836%29%2Asqrt%286%29\" Break up the square roots using the identity \"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29\"
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\n" ); document.write( " \"6%2Asqrt%286%29\" Take the square root of the perfect square 36 to get 6
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\n" ); document.write( " So the expression \"sqrt%28216%29\" simplifies to \"6%2Asqrt%286%29\"
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\n" ); document.write( " ----------------------------
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\n" ); document.write( " Notice if we evaluate the square root of 216 with a calculator we get
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\n" ); document.write( " \"sqrt%28216%29=14.6969384566991\"
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\n" ); document.write( " and if we evaluate \"6%2Asqrt%286%29\" we get
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\n" ); document.write( " \"6%2Asqrt%286%29=14.6969384566991\"
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\n" ); document.write( " This shows that \"sqrt%28216%29=6%2Asqrt%286%29\". So this verifies our answer

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\n" ); document.write( "\n" ); document.write( "For more help/practice with simplifying square roots, check out this solver: http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver \n" ); document.write( "
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