1 last square root :
Rationalize the denominator
5/sqrt[3]+sqrt[5]=
5*sqrt[3]-sqrt[5]/ sqrt[3]sqrt5[5]*sqrt[3]-sqrt[5]=
5sqrt[3]-5sqrt[5]/sqrt[9]-sqrt[15]+sqrt[15]- sqrt[25]=
5sqrt[3]-5sqrt[5]/-16 =
5sqrt[3]-5sqrt[5]/ -2
To rationalize the denominator in the expression (5/sqrt[3] + sqrt[5]), we need to eliminate the square root (radical) in the denominator.
First, we multiply the numerator and denominator by the conjugate of the denominator, which is sqrt[3] - sqrt[5].
(5/sqrt[3] + sqrt[5]) * (sqrt[3] - sqrt[5]) / (sqrt[3] - sqrt[5])
Using the distributive property, we can expand the numerator:
(5 * sqrt[3] - 5 * sqrt[5]) / (sqrt[3] - sqrt[5])
Now, we need to simplify the denominator. To do this, we use the difference of squares formula, which states that (a^2 - b^2) = (a + b)(a - b).
In this case, a = sqrt[3] and b = sqrt[5]:
(sqrt[3] - sqrt[5])(sqrt[3] + sqrt[5]) = (sqrt[3])^2 - (sqrt[5])^2 = 3 - 5 = -2
So, the simplified expression becomes:
(5 * sqrt[3] - 5 * sqrt[5]) / (-2)
Therefore, the rationalized form of the expression (5/sqrt[3] + sqrt[5]) is (5 * sqrt[3] - 5 * sqrt[5]) / (-2).