rationalize the denominator in the following radicals and collect the like terms
6√6y/ 2√7
To rationalize the denominator, we need to multiply the numerator and denominator by the conjugate of the denominator. The conjugate of √7 is -√7.
So, the rationalized form will be:
(6√6y/2√7) * (-√7/-√7)
Multiplying the numerators and denominators, we get:
(-6√6y√7)/(-2√7√7)
Simplifying the expression, we have:
-6√6y√7 / -2(√7)^2
In the denominator, (√7)^2 simplifies to just 7:
-6√6y√7 / -2(7)
Thus, the simplified rationalized form is:
-6√6y√7 / -14
Now, let's collect the like terms in the numerator:
-6√6y√7 can be written as -6√(6 * 7) * y
Simplifying further, we have:
-6√42 * y / -14
Finally, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:
(-6/2)√42 * y / (-14/2)
This simplifies to:
-3√42 * y / -7
Therefore, the rationalized denominator and collected like terms can be written as:
(3√42 * y) / 7