how would i do this square root simplification?
SQRT(4x^4 + 36x^2 + 81)
How would you do this problem to get
2x^2 + 9
???
Top 2 Answers
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(a+b)^2
= a^2 + 2ab + b^2
In this case, 4x^4 = a^2, so 2x^2 = a
81 = b^2 so b = 9
It works because 2ab = 2*2x^2*9 = 36x^2, which is the middle term.
So
SQRT(4x^4 + 36x^2 + 81)
= SQRT(2x^2 + 9)^2
= 2x^2 + 9
I hope this helps!
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SQRT(4x^4 + 36x^2 + 81) =
Replace 2x^2 = A
Then
A^2 + 18A + 81 =
SQRT( A^2 + 2*9A + 9^2 ) =
SQRT( (A+9)^2 ) =
you cancel the SQRT and the SQ and you get
A+9 but A equals 2x^2
Then replace
2X^2 + 9
Voila! The Answer
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