Okay, let's see. The problem is to compute the product of the number 5 + √3 and its radical conjugate. Hmm, radical conjugate... I think that's the term used when you have a binomial with a radical, and the conjugate would be changing the sign of the radical part. So for example, if you have a + √b, the conjugate would be a - √b. Let me confirm that. Yeah, I remember that the conjugate of a binomial expression with a radical is obtained by changing the sign of the radical term. So in this case, the radical conjugate of 5 + √3 would be 5 - √3. 

So the problem is asking for the product of these two numbers. That is, (5 + √3)(5 - √3). I think this is a difference of squares situation. Remember, when you multiply a binomial by its conjugate, the result is a^2 - b^2. Let me recall the formula: (a + b)(a - b) = a² - b². Yes, that's right. So applying that here, a would be 5 and b would be √3. 

So substituting into the formula, we get (5)² - (√3)². Let's compute that. 5 squared is 25, and (√3) squared is 3. So 25 - 3 equals 22. Therefore, the product should be 22. 

Wait, let me double-check to make sure I didn't make a mistake. Let's expand the product manually to verify. 

(5 + √3)(5 - √3) = 5*5 + 5*(-√3) + √3*5 + √3*(-√3). 

Calculating each term:

5*5 = 25

5*(-√3) = -5√3

√3*5 = 5√3

√3*(-√3) = - (√3 * √3) = -3

Now, adding all these terms together: 25 - 5√3 + 5√3 - 3. 

The -5√3 and +5√3 cancel each other out, leaving 25 - 3 = 22. 

Yes, that's correct. The middle terms indeed cancel, which confirms the use of the difference of squares formula. So the answer is 22. 

I don't see any mistakes in the reasoning. The key here was recognizing that the radical conjugate is the number with the opposite sign before the radical, and then applying the difference of squares formula. Multiplying them out step by step also confirmed that the result is 22. 

Therefore, the product of 5 + √3 and its radical conjugate is 22.
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