Question

how do you simply the cube root of 56x^14 and can you show work too please?

Answer 1

Make the factors of 56..

Can you do that??

Answer 2

yes. 2 and 28 , 4 and 14, 7 and 8 @waterineyes

Answer 3

is that right?

Answer 4

Yes it is but if you want then you can again factors them like :

You have said that 56 = 8 and 7

but here you can make factors for 8 too..

8 = 2 and 2 and 2:

So: Finally : \(56 = 2 \times 2 \times \times 2 \times 7\)

Right ??

Answer 5

This process is called Prime Factorization of a number...

Answer 6

yes. i get that.

Answer 7

dont i find 3 numbers that are the same which is 2 2 2

Answer 8

Now there is one rule of cube root that you can pull out the number if and only if they are thrice in the cube root:

For example :

\[\sqrt[3]{4 \times 5 \times 4 \times 4 \times 7}\]

Here 4 is three times inside the cube root bracket, so you can pull out 4 here..

Yes dear, you are to find 3 same numbers here so that you can take cube root correctly and efficiently..

Answer 9

okay, so now i can pull out 2 2 2 but where do i put them at?

Answer 10

So:
\[\sqrt[3]{4 \times 5 \times 4 \times 4 \times 7} = 4 \sqrt[3]{ 5 \times 7} \implies 4 \sqrt[3]{35}\]

Answer 11

Out of 3 only one 2 you can put out...

Answer 12

im so confused.

Answer 13

See :

\[\sqrt[3]{2 \times 2 \times 2} \implies \color{green}{2}\]

Answer 14

okay.. gosh im dumb. i dont understand what to do after that.

Answer 15

Cube means 3...

When you will see three same numbers inside the cube root bracket you will put out one out of them and once you pull out, you will not write then the same numbers inside the cube roots brackets..