Question

√(x+1)-(x-1)
Could someone explain how that equation simplifies to 2√x?

Answer 1

Is it\[\sqrt{(x +1)}-(x -1)\]

Answer 2

I typed the question wrong √(x+1)^2-(x-1)^2

Could someone explain how that equation simplifies to 2√x

Answer 3

I thought as much!

Answer 4

So it's\[\sqrt{(x +1)^{2}-(x -1)^{2}}\]Is this correct?

Answer 5

Yes

Answer 6

OK so do you know how to simplify the expression inside the root? You have two options: i). expand and collect like terms, or ii). factor by difference of squares method.

Choose a method.

Answer 7

I'm okay with both. Whatever simpler to explain would be nice.

Answer 8

Both are simple. your choice.

Answer 9

Collect like terms please then

Answer 10

OK then, do you know how to do that?

Answer 11

Is 4x correct?

Answer 12

Yes! so then we have\[\sqrt{4x}\]Do you know the next step to simplify this?

Answer 13

Sqrt 2*2*x?

Answer 14

\[\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}\]

Answer 15

So then by this rule\[\sqrt{4x}=\sqrt{4}\sqrt{x}\]Correct?

Answer 16

Oh~ I see!

Answer 17

Thank you so much for your kind help!

Answer 18

Very Welcome!