rationalize the denominator in the following radicals and collect the like terms
6y√27x / √9x
To rationalize the denominator, you need to get rid of the radical (√9x) in the denominator. This can be done by multiplying both the numerator and denominator by the conjugate of the denominator, which in this case is (√9x).
The conjugate of (√9x) is (-√9x).
So, multiply the numerator and denominator by (-√9x):
(6y√27x) * (-√9x) / (√9x) * (-√9x)
Simplifying the fractions:
(-6y√(27x^2))/(√(9x^2))
Now, let's simplify the radical expressions inside the numerator:
-6y√(27x^2) = -6y√(9 * 3 * x^2) = -6y * 3x *√3 = -18xy√3
The simplified expression becomes:
-18xy√3 / (√(9x^2))
Now, the denominator √(9x^2) can be further simplified as √9 * √x^2 = 3x
So, the final simplified expression is:
-18xy√3 / 3x
Now, let's collect the like terms:
-18xy√3 / 3x
= (-18xy / 3x) * √3
= -6y√3