Ratinalize the denominator. Assume all varibles represent positive numbers.
Sqrt(18)/x
To rationalize the denominator of the expression sqrt(18) / x, we need to get rid of the radical in the denominator, as radicals in the denominator are not considered rationalized.
To do this, we multiply both the numerator and denominator by a suitable quantity that will eliminate the radical. In this case, we can multiply both the numerator and denominator by sqrt(18) to get:
[sqrt(18) * sqrt(18)] / (x * sqrt(18))
The square root of 18 can be simplified as sqrt(18) = sqrt(9 * 2) = sqrt(9) * sqrt(2) = 3 * sqrt(2). Therefore, we can rewrite the expression as:
[3 * sqrt(2) * 3 * sqrt(2)] / (x * 3 * sqrt(2))
Simplifying further, we have:
9 * 2 / (3 * x * sqrt(2))
This simplifies to:
18 / (3 * x * sqrt(2))
And finally:
6 / (x * sqrt(2))
So, the rationalized form of the expression sqrt(18) / x is 6 / (x * sqrt(2)).