SOLUTION: Simplify: sqrt 45x^3y^4/16x^2 Thank you.

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Question 1171812: Simplify: sqrt 45x^3y^4/16x^2
Thank you.
Found 2 solutions by math_tutor2020, Theo:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Assuming x > 0 and y > 0, we can say

sqrt%28%2845x%5E3y%5E4%29%2F%2816x%5E2%29%29

%28sqrt%2845x%5E3y%5E4%29%29%2F%28sqrt%2816x%5E2%29%29 Use the rule that sqrt%28a%2Fb%29+=+sqrt%28a%29%2Fsqrt%28b%29

%28sqrt%289%2A5%2Ax%5E2%2Ax%2Ay%5E4%29%29%2F%28sqrt%28%284x%29%5E2%29%29

%28sqrt%28%289x%5E2y%5E4%29%2A%285x%29%29%29%2F%284x%29

%28sqrt%28%283xy%5E2%29%5E2%2A5x%29%29%2F%284x%29

%28sqrt%28%283xy%5E2%29%5E2%29%2Asqrt%285x%29%29%2F%284x%29 Use the rule that sqrt%28a%2Ab%29+=+sqrt%28a%29%2Asqrt%28b%29

%283xy%5E2%2Asqrt%285x%29%29%2F%284x%29

%283y%5E2%2Asqrt%285x%29%29%2F%284%29

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Answer: %283y%5E2%2Asqrt%285x%29%29%2F%284%29


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
see my worksheet.

step 1 shows the original problem.
step 2 divides x^3 by x^2 to get x.
step 3 takes the square root of y^4 and the square root of 16 and moves them out from within the square root sign. this is because the square root of y^4 is equal to y^2 and the square root of 16 is equal to 4.
step 4 breaks up 45 into 5 * 9.
step 5 takes sqrt 9 and moves it out from within the square root sign. this is because square root of 9 is equal to 3.

the final simplification is step 5.
i can't see any other way to simplify it further.
i checked with random numbers (7 for x and 15 for y) and got the same answer from both the original expression and the final expression.
this confirms the simplification was done correctly.

you can check it for yourself.
just replace x with 7 and y with 15.
you should get 998.3384634 from both the original expression (step 1) and the final expression (step 5).