If √24 + √96 - √600 = y√6, find the value of y

Answer Details

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.