No. I think what HallsofIvy is trying to tell you is that you have to multiply by the conjugate twice. See my post in this thread.phrox said:The only thing I see you can do with that is square it I guess?I'm not sure... Subbing in 4 will just make it 0.
You are not posting your working, so I have to guess. It sounds like you went through the full multiplication top and bottom each time. Don't do that. Multiply top and bottom by that expression which removes the radical from the denominator, but in the numerator just leave it as a product of two radical expressions. don't multiply that out. Now do the same for the radical expression which is the original numerator - multiply top and bottom by its radical 'conjugate'. You should now have an expression which is a product of two terms in the numerator (one being the conjugate of the original denominator, and the other not involving a radical) and similarly two terms in the denominator.phrox said:By rationalize do you mean multiply the conjugate? I don't see how you can rationalize (multiply top and bottom by the root), but you say you only do it to the top and then only do it to the bottom. I don't think you can do that. Also if I multiply the top conjugate and then bottom conjugate it gets REALLY messy and it can't be right.
(This is all after reading your post)
A radical in a limit is an expression that contains a root symbol, such as √x, and is used to represent a number or variable that is being taken to a certain power in a limit calculation.
To simplify a radical in a limit, you can use the rules of exponents to rewrite the expression in a simpler form. This may involve factoring the number inside the radical or using the power rule to move the exponent outside of the radical.
A radical is a symbol that represents a root, while a rational exponent is a number that represents the power to which a base is raised. In a limit, both can be used interchangeably to represent the same value.
To solve a limit with two radicals, you can use the properties of limits to break the expression into smaller limits and then evaluate each one individually. You can also use substitution or algebraic manipulation to simplify the expression before taking the limit.
Yes, it is possible to have a limit with two radicals in the denominator. In this case, you can use algebraic manipulation to rationalize the denominator and simplify the expression before taking the limit.