document.write( "Question 450287: 4√10 times 3√6
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\n" ); document.write( "Please help! (showing work is preferred) Thank you so much for helping. \n" ); document.write( "

Algebra.Com's Answer #309748 by Leaf W.(135) $\"\"$ $\"About$

You can put this solution on YOUR website!
Multiplying square roots is very much like multiplying with variables. For example, if you have to multiply 2a and 10b, you would do (2*10)(a*b) = (20)(ab) = 20ab. In the same way, if you have $\"asqrt%28b%29%2Acsqrt%28d%29\"$ , you would turn that into $\"%28a%2Ac%29%28sqrt%28b%2Ad%29%29\"$ ... basically, you multiply whatever is inside the square root sign together and whatever is outside the square root sign together.
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\n" ); document.write( "Next you have to simplify the square root by pulling whatever you can out.
\n" ); document.write( "First, factor the 60 in the square root:
\n" ); document.write( " $\"12sqrt%2860%29+=+12sqrt%282%2A2%2A3%2A5%29\"$
\n" ); document.write( "Next, for every pair of identical factors within the square root (such as 2 and 2), you can pull them out to equal one of the same factor outside of the square root; for example, in $\"3sqrt%282%2A3%2A3%2A7%29\"$ , you have two threes, so you can pull one out to equal $\"3%2A3sqrt%282%2A7%29\"$ , or $\"9sqrt%2814%29\"$
\n" ); document.write( "In this case, you have two twos, so you can pull out a two:
\n" ); document.write( " $\"12sqrt%282%2A2%2A3%2A5%29+=+12%2A2sqrt%283%2A5%29+=+24sqrt%2815%29\"$
\n" ); document.write( "Since three and five are different factors, you could not pull anything out.
\n" ); document.write( "==> Therefore, the final answer is $\"24sqrt%2815%29\"$
\n" ); document.write( "Hope that makes sense! =)
\n" ); document.write( "--Leaf \n" ); document.write( "

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