SOLUTION: {{{ 7sqrt(72) - 2sqrt(50)}}} {{{ 2^3sqrt(54x^4) - 3^3sqrt(16x^4)}}} {{{ 6sqrt(98) - 9sqrt(32) - 3sqrt(200)}}} {{{sqrt(12/21)}}} {{{ 5^3sqrt(16) + 2^3sqrt(128)}}} {{{

Algebra ->  Algebra  -> Radicals -> SOLUTION: {{{ 7sqrt(72) - 2sqrt(50)}}} {{{ 2^3sqrt(54x^4) - 3^3sqrt(16x^4)}}} {{{ 6sqrt(98) - 9sqrt(32) - 3sqrt(200)}}} {{{sqrt(12/21)}}} {{{ 5^3sqrt(16) + 2^3sqrt(128)}}} {{{      Log On

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Question 119046: +7sqrt%2872%29+-+2sqrt%2850%29
+2%5E3sqrt%2854x%5E4%29+-+3%5E3sqrt%2816x%5E4%29
+6sqrt%2898%29+-+9sqrt%2832%29+-+3sqrt%28200%29
sqrt%2812%2F21%29
+5%5E3sqrt%2816%29+%2B+2%5E3sqrt%28128%29
+2%2Fsqrt%286%29
I know the limit is four a day, but I really am having trouble understanding radicals. Any help would be greatly appreciated. Thanks so much!!!


Answer by jim_thompson5910(28546) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first three to help you get started.


#1

7%2Asqrt%2872%29-2%2Asqrt%2850%29 Start with the given expression


7%2A6%2Asqrt%282%29-2%2Asqrt%2850%29 Simplify sqrt%2872%29 to get 6%2Asqrt%282%29. Note: If you need help with simplifying square roots, check out this solver.


7%2A6%2Asqrt%282%29-2%2A5%2Asqrt%282%29 Simplify sqrt%2850%29 to get 5%2Asqrt%282%29.


42%2Asqrt%282%29-2%2A5%2Asqrt%282%29 Multiply 7 and 6 to get 42.

42%2Asqrt%282%29-10%2Asqrt%282%29 Multiply 2 and 5 to get 10.

Since we have the common term sqrt%282%29, we can combine like terms

%2842-10%29sqrt%282%29 Combine like terms. Remember, 5x%2B3x-4x=%285%2B3-4%29x=4x


32%2Asqrt%282%29 Now simplify 42-10 to get 32

So 7%2Asqrt%2872%29-2%2Asqrt%2850%29 simplifies to 32%2Asqrt%282%29. In other words, 7%2Asqrt%2872%29-2%2Asqrt%2850%29=32%2Asqrt%282%29








+2%5E3sqrt%2854x%5E4%29+-+3%5E3sqrt%2816x%5E4%29 Start with the given expression



+8%2Asqrt%2854x%5E4%29+-+27%2Asqrt%2816x%5E4%29 Evaluate 2%5E3 to get 8. Evaluate 3%5E3 to get 27



+8%2Asqrt%289%2A6%2Ax%5E2%2Ax%5E2%29+-+27%2Asqrt%284%2A4%2Ax%5E2%2Ax%5E2%29 Factor 54x%5E4 into 9%2A6%2Ax%5E2%2Ax%5E2. Factor 16x%5E4 into 4%2A4%2Ax%5E2%2Ax%5E2




Break up the square roots



+8%2A3%2Asqrt%286%29%2Ax%2Ax+-+27%2A4%2Ax%2Ax Take the square root.



+24x%5E2%2Asqrt%286%29+-+108x%5E2 Multiply



So +2%5E3sqrt%2854x%5E4%29+-+3%5E3sqrt%2816x%5E4%29 simplifies to 24x%5E2%2Asqrt%286%29+-+108x%5E2.

In other words, +2%5E3sqrt%2854x%5E4%29+-+3%5E3sqrt%2816x%5E4%29=24x%5E2%2Asqrt%286%29+-+108x%5E2






#3




6%2Asqrt%2898%29-9%2Asqrt%2832%29-3%2Asqrt%28200%29 Start with the given expression


6%2A7%2Asqrt%282%29-9%2Asqrt%2832%29-3%2Asqrt%28200%29 Simplify sqrt%2898%29 to get 7%2Asqrt%282%29. Note: If you need help with simplifying square roots, check out this solver.


6%2A7%2Asqrt%282%29-9%2A4%2Asqrt%282%29-3%2Asqrt%28200%29 Simplify sqrt%2832%29 to get 4%2Asqrt%282%29.


6%2A7%2Asqrt%282%29-9%2A4%2Asqrt%282%29-3%2A10%2Asqrt%282%29 Simplify sqrt%28200%29 to get 10%2Asqrt%282%29.


42%2Asqrt%282%29-9%2A4%2Asqrt%282%29-3%2A10%2Asqrt%282%29 Multiply 6 and 7 to get 42.

42%2Asqrt%282%29-36%2Asqrt%282%29-3%2A10%2Asqrt%282%29 Multiply 9 and 4 to get 36.

42%2Asqrt%282%29-36%2Asqrt%282%29-30%2Asqrt%282%29 Multiply 3 and 10 to get 30.

Since we have the common term sqrt%282%29, we can combine like terms

%2842-36-30%29sqrt%282%29 Combine like terms. Remember, 5x%2B3x-4x=%285%2B3-4%29x=4x


-24%2Asqrt%282%29 Now simplify 42-36-30 to get -24

So 6%2Asqrt%2898%29-9%2Asqrt%2832%29-3%2Asqrt%28200%29 simplifies to -24%2Asqrt%282%29. In other words, 6%2Asqrt%2898%29-9%2Asqrt%2832%29-3%2Asqrt%28200%29=-24%2Asqrt%282%29