rationalize the denominator sqrt 5/ (5+sqrt6)
To rationalize the denominator of the given expression, we need to get rid of the square root in the denominator.
The general method involves multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of a binomial is obtained by changing the sign between the terms. In this case, the conjugate of (5 + √6) is (5 - √6).
So, we can multiply the numerator and denominator of the expression by the conjugate:
(sqrt(5) / (5 + √6)) * ((5 - √6) / (5 - √6))
Now, let's simplify this expression:
(sqrt(5) * (5 - √6)) / ((5 + √6) * (5 - √6))
In the denominator, we have a difference of squares, which simplifies to:
(5^2 - (√6)^2) = (25 - 6) = 19
The numerator remains as:
sqrt(5) * (5 - √6) = 5√5 - √30
Therefore, the simplified rationalized form of sqrt(5)/(5 + √6) is:
(5√5 - √30) / 19