Question

Please Help and Explain if Possible?


Simply 3√x7

Answer 1

the little 3 in front of the radical sign means the third root or "cube root"
I would expand x^7 to
(x*x*x) * (x*x*x) * x
inside the radical. then "pull out" any triplets

Answer 2

when you pull out a triplet, outside the radical sign it "shrinks" to just one x

Answer 3

so it would be D?

Answer 4

how many "triplets" (of x) are inside the radical sign ?

Answer 5

2?

Answer 6

yes x^7 can be written as
(x*x*x) * (x*x*x) * x

and there are two "triplets"
if you pull them out of the radical, each one becomes a single x on the outside
how many x's will be on the outside of the radical sign?

Answer 7

6?

Answer 8

each triplet on the inside becomes a single x on the outside

Answer 9

how many x's will be on the outside of the radical sign?
(after we pull out the two triplets)

Answer 10

well there would be 7 if all of them counted. But if you don't count the triplets there would be 1

Answer 11

Notice this
\[ \sqrt[3]{x\cdot x \cdot x}= x \]
the 3 inside can be "pulled out" and turned into 1 x on the out side

in your problem, pull out two triples
\[ \sqrt[3]{(x\cdot x \cdot x) \cdot (x\cdot x \cdot x) \cdot x}\]

Answer 12

so there would be 3?

Answer 13

it turns into
\[ x \cdot x \cdot \sqrt[3]{x} \\ x^2 \sqrt[3]{x}\]