Answer: [tex]2\sqrt{2}[/tex]
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Explanation:
Let's say we replace every copy of [tex]\sqrt{2}[/tex] with x
Doing so means we have the expression 5x-3x. That simplifies to 2x.
The last thing to do is replace the x with [tex]\sqrt{2}[/tex] and that's how we end up with [tex]2\sqrt{2}[/tex] as the final answer.
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In short: we subtract the numbers out front, and then tack on a root 2 at the end.
As another example, [tex]19\sqrt{2}-11\sqrt{2} = (19-11)\sqrt{2} = 8\sqrt{2}[/tex]
This is basically the same as saying 19x-11x = (19-11)x = 8x where [tex]x = \sqrt{2}[/tex]
