I need help on how to simplify √3:(54) please help!!?
√3:(54a^7b^4)
(the 3 is in the place of 2 in a square root)
So first, I separate the problem into 3 parts:
√3:(54) , √3:(a^7), √3:(b^4)
I know how to simplify the last two, but not the first one.
For √3:(a^7), i got: a^2√3:(a)
For √3:(b^4), i got: b√3:(b)
I think those are right, but then I don't know about the first one.
Do I first try to find three of the same numbers that equal to 54? But it would be a decimal...
Please help! Thanks!!
Update:*√3:(54a^7b^4) would be ³√(54a^7b^4)
Update 3:@husoski ahhhh FINALLY, THANK U SO MUCH!
I didn't know that you had to factor the 54 into primes, so I was factoring into numbers like 9 and 6. Thanks again :)
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Verified answer
Take the 54, a^7 and b^4 separately, as you already did. To simplify roots, factor integers into primes. Then group powers into cubes, multiplied by any leftover factors.
54 = 27*2 = (3^3) * 2
a^7 = (a^6)*a
b^4 = (b^3)*b
The parenthesized factors are perfect cubes, and the unparenthesized factors have exponents less than 3 and don't simplify for cube root purposes. so:
³√(54 a^7 b^4) = 3a²b ³√(2ab)
As you said, you got the variables right. For exact results with integers, work with the prime factorization of the coefficients, and treat each prime as a different "variable."