SOLUTION: I really do not understand these problems please help Rewrite the following in simlified radical form 1)square root 54x^4 Simplify the following expressions as much as possibl

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: I really do not understand these problems please help Rewrite the following in simlified radical form 1)square root 54x^4 Simplify the following expressions as much as possibl      Log On

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Question 195463: I really do not understand these problems please help
Rewrite the following in simlified radical form
1)square root 54x^4
Simplify the following expressions as much as possible
2)6w square root63u^3-usquare root7uw^2
Rationalize the denominator and simplify
3)square root21/square root 77
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


sqrt%2854x%5E4%29 Start with the given expression


sqrt%289%2A6x%5E4%29 Factor 54 into 9%2A6. Note: 9 is the largest perfect square factor of 54


sqrt%289%2A6%2Ax%5E2%2Ax%5E2%29 Factor x%5E4 into x%5E2%2Ax%5E2


sqrt%289%29%2Asqrt%286%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29 Break up the square root.


3%2Asqrt%286%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29 Take the square root of 9 to get 3


3%2Asqrt%286%29%2Ax%2Ax Take the square root of x%5E2 to get "x"


3x%2Asqrt%286%29 Multiply


So sqrt%2854x%5E4%29=3x%2Asqrt%286%29 where x%3E=0





# 2


6w%2Asqrt%2863%2Au%5E3%29-u%2Asqrt%287%2Auw%5E2%29 Start with the given expression


6w%2A3u%2Asqrt%287u%29-u%2Asqrt%287%2Auw%5E2%29 Simplify sqrt%2863%2Au%5E3%29 to get 3%2Au%2Asqrt%287%2Au%29


6w%2A3u%2Asqrt%287u%29-uw%2Asqrt%287u%29 Simplify sqrt%287%2Auw%5E2%29 to get w%2Asqrt%287%2Au%29


18uw%2Asqrt%287u%29-uw%2Asqrt%287u%29 Multiply


%2818-1%29uw%2Asqrt%287u%29 Factor out the GCF uw%2Asqrt%287u%29


17uw%2Asqrt%287u%29 Combine like terms.



So 6w%2Asqrt%2863%2Au%5E3%29-u%2Asqrt%287%2Auw%5E2%29=17uw%2Asqrt%287u%29 where every variable is non negative.




# 3

sqrt%2821%29%2Fsqrt%2877%29 Start with the given expression


%28sqrt%2821%29sqrt%2877%29%29%2F%28sqrt%2877%29sqrt%2877%29%29 Multiply both the numerator and denominator by sqrt%2877%29


%28sqrt%2821%29sqrt%2877%29%29%2F%2877%29 Multiply sqrt%2877%29sqrt%2877%29 to get sqrt%2877%29sqrt%2877%29=%28sqrt%2877%29%29%5E2=77


%287%2Asqrt%2833%29%29%2F%2877%29 Multiply sqrt%2821%29sqrt%2877%29 to get sqrt%2821%29sqrt%2877%29=sqrt%2821%2A77%29=sqrt%287%2A3%2A7%2A11%29=sqrt%2849%2A33%29=7%2Asqrt%2833%29


sqrt%2833%29%2F11 Reduce


So sqrt%2821%29%2Fsqrt%2877%29=sqrt%2833%29%2F11