Simplify as much as possible

[Guest]

I think I got these two but would like to double check before turning in. Thanks!! Andrea
BTW, I apologize in advance for any misunderstanding in my notation as it is hard to do square roots and exponents in the same problem; it is much easier to read with the Math Type program.


(A)
2 sqrt x + 3(x + 1)^2-sqrt(4x) + x^2
2 sqrt x + 3(x^2 + 2x + 1) - sqrt(4x) + x^2
2 sqrt x + 3x^2 + 6x + 3) - sqrt(4x) + x^2
2 sqrt x - 2 sqrt x + 3x^2 + x^2 + 6x + 3
4x^2 + 6x + 3


(B)
sqrt(64x^5) / sqrt(121x^7)
8x^2(sqrt x) / 11x^2(sqrt x^3)

 

[Mrspi]

I think I got these two but would like to double check before turning in. Thanks!! Andrea
BTW, I apologize in advance for any misunderstanding in my notation as it is hard to do square roots and exponents in the same problem; it is much easier to read with the Math Type program.


(A)
2 sqrt x + 3(x + 1)^2-sqrt(4x) + x^2
2 sqrt x + 3(x^2 + 2x + 1) - sqrt(4x) + x^2
2 sqrt x + 3x^2 + 6x + 3) - sqrt(4x) + x^2
2 sqrt x - 2 sqrt x + 3x^2 + x^2 + 6x + 3
4x^2 + 6x + 3


(B)
sqrt(64x^5) / sqrt(121x^7)
8x^2(sqrt x) / 11x^2(sqrt x^3)

(A) looks good

(B) You didn't simplify the radical in the denominator as much as you could. sqrt(x^3) still contains a perfect square factor of x^2, so the denominator SHOULD simplify to 11 x^3 sqrt(x).

That will give you

8 x^2 sqrt(x)
---------------
11 x^3 sqrt(x)

Now, you've got some common factors that can be divided out of numerator and denominator.......

 

[Denis]

Hey, you're sure a quick learner, Andrea :wink: