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.