SOLUTION: Simplify (be sure to rationalize all denominators) 10. 3b[SQRT(27a^5b)] + 2a[SQRT(3a^3b^3)] Here is how I wrote the steps. 1. 3b[SQRT(27a^5b)] + 2a[SQRT(3a^3b^3)] 2. 3

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: Simplify (be sure to rationalize all denominators) 10. 3b[SQRT(27a^5b)] + 2a[SQRT(3a^3b^3)] Here is how I wrote the steps. 1. 3b[SQRT(27a^5b)] + 2a[SQRT(3a^3b^3)] 2. 3      Log On

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Question 83596: Simplify (be sure to rationalize all denominators)
10. 3b[SQRT(27a^5b)] + 2a[SQRT(3a^3b^3)]
Here is how I wrote the steps.
1. 3b[SQRT(27a^5b)] + 2a[SQRT(3a^3b^3)]
2. 3b[3a^2SQRT(3ab)] + 2a[a^2b^2SQRT(3ab)]
3. [9a^2+2a^3b^2][SQRT(3ab)]
I am told that there is a small error in the second step. I was also told to notice in the second term,I have SQRT(3a^3b^3).If I remove the perfect square roots,I'll remove only ab, not a^2b^2. I thought that I had the correct answer and am wonder what the correct step and answer are. Thank you for any help you have!

Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
3b%2Asqrt%2827a%5E5b%29%2B2a%2Asqrt%283a%5E3b%5E3%29
3b%2Asqrt%283%2A9%2Aa%2Aa%5E4%2Ab%29+%2B+2a%2Asqrt%283%2Aa%2Aa%5E2%2Ab%2Ab%5E2%29Take the square root of the squares.
3b%2A3%2Aa%5E2%2Asqrt%283ab%29+%2B+2a%2Aa%2Ab%2Asqrt%283ab%29 Simplify.
9a%5E2b%2Asqrt%283ab%29+%2B+2a%5E2b%2Asqrt%283ab%29 Add the terms.
11a%5E2b%2Asqrt%283ab%29
N.B. In your second step, you failed to take the square root of the a%5E2 and the b%5E2 in the second term when you brought them outside of the radical.

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
+3b%28sqrt%2827a%5E5b%29%29+%2B+2a%28sqrt%283a%5E3b%5E3%29%29 Start with the given expression

+3b%28sqrt%289%2A3%2Aa%5E2%2Aa%5E2%2Aa%2Ab%29%29+%2B+2a%28sqrt%283%2Aa%5E2%2Aa%2Ab%5E2%2Ab%29%29 Factor 27 into 9*3, a%5E5 into a%5E2%2Aa%5E2%2Aa, a%5E3 into a%5E2%2Aa, and b%5E3 into b%5E2%2Ab

+3b%28sqrt%289%29%2Asqrt%283%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%2Ab%29%29+%2B+2a%28sqrt%283%29%2Asqrt%28a%5E2%29%2Asqrt%28a%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29%29 Break up the square roots


+3b%283%2Asqrt%283%29%2Aa%2Aa%2Asqrt%28a%2Ab%29%29+%2B+2a%28sqrt%283%29%2Aa%2Asqrt%28a%29%2Ab%2Asqrt%28b%29%29 Take the square root of all the perfect squares


+3b%283a%5E2%2Asqrt%283%29%2Asqrt%28a%2Ab%29%29+%2B+2a%28ab%2Asqrt%283%29%2Asqrt%28a%29%2Asqrt%28b%29%29 Multiply


+3b%283a%5E2%2Asqrt%283ab%29%29+%2B+2a%28ab%2Asqrt%283ab%29%29 Combine any left over square roots

+9a%5E2b%2Asqrt%283ab%29+%2B+2a%5E2b%2Asqrt%283ab%29%29 Multiply

+%289a%5E2b%2B2a%5E2b%29%2Asqrt%283ab%29%29+ Combine like terms

+11a%5E2b%2Asqrt%283ab%29+ Add. So this is the simplified expression