Rationalize the denominator and simplify: 4-sqrt 3 /sqrt 5
To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator.
Conjugate of sqrt 5 is -sqrt 5.
So, we multiply by -sqrt 5 / -sqrt 5:
(4 - sqrt 3) / sqrt 5 * (-sqrt 5 / -sqrt 5)
= (-4sqrt 5 - sqrt 3 * -sqrt 5) / 5
= (-4sqrt 5 + sqrt 15) / 5
Therefore, the rationalized and simplified form of (4 - sqrt 3) / sqrt 5 is (-4sqrt 5 + sqrt 15) / 5.