Question

Is the simplified form of 2square root of 3 + 3square root of 3 rational?

Yes
No

Answer 1

@whpalmer4

Answer 2

@undeadknight26

Answer 3

No it is not rational :)

Answer 4

thanks:) @Superpoopergirl

Answer 5

No problem:)

Answer 6

You can determine if it is rational by examining the expression for square root signs. If you find one, and the expression within it is reduced as far as it can be, then it is not rational. After you simplify \[2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}\]you are still left with something under a square root sign, and you cannot simplify it away, so the expression is not rational. As you hopefully recall, for something to be rational it must be expressible as the ratio of two integers, but it is possible to show that any simplified square root which still contains a radical cannot be expressed as such a ratio.