SOLUTION: This question isn't from a book, but from a summer packet. {{{ sqrt(8x^3) + sqrt(2x) }}} I've only gotten so far as breaking down the first half of the formula so that I'm le

Algebra ->  Radicals -> SOLUTION: This question isn't from a book, but from a summer packet. {{{ sqrt(8x^3) + sqrt(2x) }}} I've only gotten so far as breaking down the first half of the formula so that I'm le      Log On


   

Question 151067: This question isn't from a book, but from a summer packet.
+sqrt%288x%5E3%29+%2B+sqrt%282x%29+
I've only gotten so far as breaking down the first half of the formula so that I'm left with:
+2%2Asqrt%282x%5E3%29+%2B+sqrt%282x%29+
I don't know what to do next!
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll start where you left off.


+2%2Asqrt%282x%5E3%29+%2B+sqrt%282x%29+ Start with the given expression.


+2%2Asqrt%282%2Ax%5E2%2Ax%29+%2B+sqrt%282x%29+ Factor 2x%5E3 into 2%2Ax%5E2%2Ax


+2%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29+%2B+sqrt%282x%29+ Break up the root.


+2%2Asqrt%282%29%2Ax%2Asqrt%28x%29+%2B+sqrt%282x%29+ Take the square root of x%5E2 to get x


+2x%2Asqrt%282x%29%2B+sqrt%282x%29+ Multiply and combine the roots.


+sqrt%282x%29%282x%2B+1%29+ Factor out the GCF sqrt%282x%29


+%282x%2B+1%29sqrt%282x%29+ Rearrange the terms.


So +sqrt%288x%5E3%29+%2B+sqrt%282x%29+ simplifies to +%282x%2B+1%29sqrt%282x%29+


In other words, +sqrt%288x%5E3%29+%2B+sqrt%282x%29+=+%282x%2B+1%29sqrt%282x%29+ where x%3E=0