rationalize

3/7-root3

would it be

21+3root3/46

To rationalize the expression (3/7-√3), we need to eliminate the square root (√3) from the denominator.

To do this, we use a method called rationalizing the denominator, which involves multiplying both the numerator and denominator by the conjugate of the denominator.

In this case, the conjugate of (√3) is (-√3).

So, we have:

(3/7-√3) * (7+√3)/(7+√3)

Now, let's simplify:

Numerator:
(3/7) * (7+√3) = 21/7 + (3√3)/7 = 3 + (√3)/7

Denominator:
(7+√3) * (7-√3) = 49 - 3 = 46

Putting it all together, we get:

(3 + (√3)/7) / 46

Therefore, the rationalized form of (3/7-√3) is (3 + (√3)/7) / 46, which is equivalent to 21 + (3√3)/46.