Question

4 (before square root ) square root 256x^6

Answer 1

\(4\sqrt{256x^{6}}\)

Find perfect squares inside the radical.

\(256 = 16^{2}\)

\(x^{2} = \left(x^{3}\right)^{2}\)

Simplify away...

Answer 2

\[\sqrt[4]{256x^6?}\]

Answer 3

@tkhunny

Answer 4

Why is that different?

Find perfect 4ths:

\(256 = 4^{4}\)

\(x^{6} = x^{4}\cdot x^{2}\) <== Be VERY careful with this piece.

Answer 5

sorry i wrote it wrong the first time

Answer 6

Okay, have at it.

Answer 7

\[\sqrt[4]{4x^6?}\]

Answer 8

since 256 =4^4 the 4 before the square root will cancel out

Answer 9

right? @tkhunny

Answer 10

wait would it be 1/4x^1/2 or 4/x^1/2

Answer 11

someone please help

Answer 12

?? \(\sqrt[4]{256} = \sqrt[4]{4^{4}} = 4^{4/4} = 4^{1} = 4\)

You do the 'x' part.

Answer 13

x^1/2

Answer 14

?

Answer 15

or would it be 4x^3/2?

Answer 16

Why not follow the nice, clear path?

\(\sqrt[4]{x^{6}} = \sqrt[4]{x^{4}\cdot x^{2}} = \sqrt[4]{x^{4}}\cdot\sqrt[4]{x^{2}} = x^{4/4}\cdot x^{2/4} = |x|\cdot\sqrt{|x|}\)

It's a little tricky towards the end.

Answer 17

x multiply by x^1/2

Answer 18

Well, the absolute values are necessary, but your particular exam or teacher may not care about that.

Answer 19

which equals x^3/2

Answer 20

4x^3/2 would be the answer

Answer 21

That is one possible correct form.

Answer 22

so it is correct?