document.write( "Question 343532: 7 √32 / 9 √8 \n" ); document.write( "

Algebra.Com's Answer #246347 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"7sqrt%2832%29%2F9sqrt%288%29\"$
\n" ); document.write( "As is often the case in Math, there is more than one way to simplify this expression. To me the easiest way is based on noticing that dividing 32 and 8 (which are currently inside separate square roots) results in 4 which is a prefect square!

\n" ); document.write( "So we will start by getting the 32 and the 8 into the same square root. First we'll use basic Algebra to split this fraction in two:
\n" ); document.write( " $\"%287%2F9%29%2A%28sqrt%2832%29%2Fsqrt%288%29%29\"$
\n" ); document.write( "Now we can use one of the properties of radicals:
\n" ); document.write( " $\"sqrt%28a%29%2Fsqrt%28b%29+=+sqrt%28a%2Fb%29\"$
\n" ); document.write( "to combine the square roots of the second fraction into a single square root:
\n" ); document.write( " $\"%287%2F9%29%2Asqrt%2832%2F8%29\"$
\n" ); document.write( "Now we can replace the 32/8 with a 4:
\n" ); document.write( " $\"%287%2F9%29%2Asqrt%284%29\"$
\n" ); document.write( "and the $\"sqrt%284%29\"$ with a 2:
\n" ); document.write( " $\"%287%2F9%29%2A2\"$
\n" ); document.write( "And we finish by multiplying:
\n" ); document.write( " $\"14%2F9\"$
\n" ); document.write( "(I'll leave it up to you to change this improper fraction into a mixed number.)\r
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