# 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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