Question

What is the simplified form of ... (picture in comments)

Answer 1

Can you factor out 48 first?

Answer 2

What do mean?

Answer 3

you

Answer 4

What do you mean*

Answer 5

I mean, what are the factors of 48?

Answer 6

2, 3, 4, 6, 8, 12, 16, and 24

Answer 7

Right, so I can write 48 = 16*3 also? right... ?

Answer 8

Yes.

Answer 9

Now, let us write this :

\(\sqrt{48 n^9} = \sqrt{16 * 3 * n^9} \)

Answer 10

Ok

Answer 11

Now, can I write \(\large n^9 \space \text{as} \space n^8 * n \) ?

Answer 12

Yes

Answer 13

Now, \(\large \sqrt{16*3 * n^8 * n }\)

What is the square root of 16 and that of n^8 ?

Answer 14

the suare root of 16 is 4, and i think the square root of n^8 is n, but I'm not sure.

Answer 15

yes, the square root of 16 is 4 but , square root of n^8 = \(\large (n^8)^{\cfrac{1}{2}} \)
Now multiplying 8 * 1/2 = n^4
so it is n^4

Answer 16

Ohh, ok

Answer 17

or

n^8 = n * n * n * n * n * n * n* n

square root of this will be : n * n * n * n

Answer 18

You get now : \(4n^4 \sqrt{3n}\)

Answer 19

OKay