SOLUTION: Simplify square roots: i.e. Simplify the square root of 36x^4y^5 or square root of 121x^5 divided by 9

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: Simplify square roots: i.e. Simplify the square root of 36x^4y^5 or square root of 121x^5 divided by 9      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 195716: Simplify square roots: i.e. Simplify the square root of 36x^4y^5 or square root of 121x^5 divided by 9
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



sqrt%2836%2Ax%5E4%2Ay%5E5%29 Start with the given expression.


sqrt%2836%2Ax%5E2%2Ax%5E2%2Ay%5E5%29 Factor x%5E4 into x%5E2%2Ax%5E2


sqrt%2836%2Ax%5E2%2Ax%5E2%2Ay%5E2%2Ay%5E2%2Ay%29 Factor y%5E5 into y%5E2%2Ay%5E2%2Ay


sqrt%2836%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


6%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29 Take the square root of 36 to get 6.


6%2Ax%2Ax%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29 Take the square root of x%5E2 to get x.


6%2Ax%2Ax%2Ay%2Ay%2Asqrt%28y%29 Take the square root of y%5E2 to get y.


6x%5E2y%5E2%2Asqrt%28y%29 Multiply.

==================================================

Answer:


So sqrt%2836%2Ax%5E4%2Ay%5E5%29 simplifies to 6x%5E2y%5E2%2Asqrt%28y%29


In other words, sqrt%2836%2Ax%5E4%2Ay%5E5%29=6x%5E2y%5E2%2Asqrt%28y%29 where every variable is non-negative.




# 2


sqrt%28%28121x%5E5%29%2F9%29 Start with the given expression.


%28sqrt%28121x%5E5%29%29%2Fsqrt%289%29 Break up the root.


%28sqrt%28121x%5E5%29%29%2F3 Take the square root of 9 to get 3.


sqrt%28121%2Ax%5E2%2Ax%5E2%2Ax%29%2F3 Factor x%5E5 into x%5E2%2Ax%5E2%2Ax


%28sqrt%28121%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%29%2F3 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


%2811%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%29%2F3 Take the square root of 121 to get 11.


%2811%2Ax%2Ax%2Asqrt%28x%29%29%2F3 Take the square root of x%5E2 to get x.


%2811%2F3%29x%5E2%2Asqrt%28x%29 Rearrange and multiply the terms.

==================================================

Answer:


So sqrt%28%28121x%5E5%29%2F9%29 simplifies to %2811%2F3%29x%5E2%2Asqrt%28x%29


In other words, sqrt%28%28121x%5E5%29%2F9%29=%2811%2F3%29x%5E2%2Asqrt%28x%29 where x%3E=0