To find the value of y in the given expression, let's simplify it step by step:
√24 + √96 - √600 = y√6
First, let's simplify the square roots inside the expression:
√24 = √(4 * 6) = √4 * √6 = 2√6
√96 = √(16 * 6) = √16 * √6 = 4√6
√600 = √(100 * 6) = √100 * √6 = 10√6
Now, we substitute the simplified values back into the expression:
2√6 + 4√6 - 10√6 = y√6
Combining like terms:
(2 + 4 - 10)√6 = y√6
Simplifying further:
-4√6 = y√6
Since the coefficient of √6 on both sides of the equation is the same, we can conclude that the value of y must be -4.
Therefore, y = -4.
So, the correct answer is -4.