Start by finding factors for the radical term.

We can rewrite the radical using these factors.

Simplify the first term.

Always work the math under the radical before simplifying. We can't do any math so let's see if it's factorable. This isn't factorable either so the answer is just the problem stated. 

 If you don't believe it, let  and 

Let's analyze each statement.

I.

Let's try to factor. This isn't factorable so this statement is usually false, NOT ALWAYS true.

 If you don't believe it, let  and 

The only time this is true is if  or  were  and the other variable was a perfect square. 

II. 

Let's say .  This is very true HOWEVER, what if . . Square roots don't generate negative values. Remember to do the math inside the radicand before simplifying. Only positive values and zero are possible and since there is no restriction on , all assumptions are based on  being any real number. So we can elminate this statement since question is asking ALWAYS true. 

III. The smallest integer in a radicand that generates a plausible, real number and smallest value is 0. 

From the second statement reasoning, "only positive values and zero are possible", this confirms that this statement is always true. Integers are whole numbers found on a number line. Real numbers are numbers found on a number line including all rational numbers (integers that can easily be fractions) and irrational numbers(values that can't be written as fractions). Remember, a negative number in a square root creates imaginary numbers (numbers including ). Even if you decide to say , it doesn't make statement III false.  is greater than  even though  is a smaller integer than 

Therefore III only is the correct answer.

When simplifying radicals, you want to factor the radicand and look for square numbers.

Both the  and  are not perfect squares, so the answer is just . 

When simplifying radicals, you want to factor the radicand and look for square numbers.

  is a perfect square so the answer is just . 

When simplifying radicals, you want to factor the radicand and look for square numbers.

If you aren't sure whether  can be factored, use divisibility rules. Since it's odd and not ending in , lets check if  is a possible factor. To know if a number is factorable by , you add the sum of the individual numbers in that number.

Since  is divisible by , just divide  by  and continue doing this. You should do this  more times and see that . 

Since  is a perfect square, or  we can simplify the radical as follows.

When simplifying radicals, you want to factor the radicand and look for square numbers.

 Since  is a perfect square but  is not, we can write it like this:

Remember, the other factor that's not a perfect square is left in the radicand and the square root of the perfect square is outside the radical. 

When simplifying radicals, you want to factor the radicand and look for square numbers.

Since  is a perfect square but  is not, we can write it as follows:

Remember, the other factor that's not a perfect square is left in the radicand and the square root of the perfect square is outside the radical. 

When simplifying radicals, you want to factor the radicand and look for square numbers.

Since  is a perfect square but  is not, we can write it like this:

Remember, the other factor that's not a perfect square is left in the radicand and the square root of the perfect square is outside the radical. 

If you didn't know  was a perfect square, there's a divisibility rule for . If the ones digit and hundreds digit adds up to the tens value, then it's divisibile by .  so  is divisible by  and its other factor is also . It's best to memorize perfect squares up to 

When simplifying radicals, you want to factor the radicand and look for square numbers.

It's essentially the same factor so the answer is .