how do you simplify the square root of (9a^4+18a^3+9a^2) dont assume all variables represent positive?

Answer 1

That's a lot like 9 * a^2 * (a+1)^2, so the square root is a lot like 3a(a+1) = 3a^2 + 3a.

HOWEVER, you need to put a +/- in front of the answer, to acknowledge the fact that 3a^2+3a could be negative, whereas square roots are supposed to be positive.

Answer 2

1) take the 9a^2 factor out:
9a^4+18a^3+9a^2 = 9a^2 (a^2 + 2a + 1) = 9a^2 (a+1)^2 = (3a)^2 * (a+1)^2 = {3a(a+1)}^2

2) the square root:
V(9a^4+18a^3+9a^2) = V[{3a(a+1)}^2] = 3a(a+1)

Answer 3

First factor out what is common to all terms.....9a^2
9a^2 (a^2 + 2a + 1)
sqrt of 9a^2 is 3a
sqrt of a^2 + 2a + 1 = a + 1
3a(a + 1) = 3a^2 + 3a

Answer 4

9a^4+18a^3+9a^2 = 9a^2 (a^2 +2a +1)=
9a^2(a+1)^2

sqrt of 9a^4+18a^3+9a^2 = 3a(1+a)= 3a^2 +3a

Answer 5

factor
9a²(a² + 2a + 1)
9a²(a + 1)²

√9a²(a + 1)² = ±3 * lal * l a+1 l

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Answer 6

i will assume that the sq. root encompassed all numbers: sqrt(49z^28 / 9) = sqrt(40 9/9)sqrt(z^28) = (7/3)*z^14 = 7z^14/3 so c whilst taking sq. roots of variables we purely would desire to take 0.5 of the exponent - with numbers we purely the two use a calculator or know the quantity as a suitable sq. and proceed as such. desire this permits!

Answer 7

= 3a^2 + 3a