Question

More square root problems.. They just seem to get harder and harder by not baby steps, but by leaps & bounds.. Help please..? Thanks y'all !

(picture)

Answer 1

to simplify the cube root of -16:
factor 16 into 2*2*2*2
to get a -16, we need 1 -2 or 3 -2. let's use 3 of them:
-2*-2*-2* 2
now you can take the cube root by taking out triples of the same number.

Answer 2

so the first term becomes
\[ 6\cdot -2 \sqrt[3]{2}= -12 \sqrt[3]{2} \]

Answer 3

can you find the factors of 54? and add the right number of minus signs so you get -54?

Answer 4

Well 27*2=54 & the cube root of 27 is 3 and you need an odd number of negative signs, so -3*-3*-3=-27*2=54. Am I right? (& Thanks for helping !!)

Answer 5

yes. so "pull out" the three -3's from the cube root. the 2 stays inside.
\[ \sqrt[3]{-54}= -3\sqrt[3]{2} \]

Answer 6

so the 2nd term is
\[ \frac{2}{3} \sqrt[3]{-54} = \frac{2}{3}\cdot -3\sqrt[3]{2} = -2\sqrt[3]{2}\]

Answer 7

can you do the last term?

Answer 8

The last term of cbrt250=5cbrt2. Then you multiply that by -5 and you are left with -25cbrt2. Right? And then you add them together to get 11cbrt2. Right? Or did I get ahead of myself?

Answer 9

looks good except for the sum
isn't is -12 cbrt(2) - 2 cbrt(2) -25cbrt(2)

Answer 10

Oh right, I switched the last to positive, but I forgot I had included the sign when I multiplied. So the actual sum is -39cbrt2