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

Analyze the question: We need to simplify each surd into a multiple of √6, then add and subtract the coefficients.

Concept: Simplify a surd by pulling out perfect-square factors: √(a²b) = a√b.

Solution:

• √24 = √(4 × 6) = 2√6
• √96 = √(16 × 6) = 4√6
• √600 = √(100 × 6) = 10√6

Substitute:

2√6 + 4√6 − 10√6 = (2 + 4 − 10)√6 = −4√6

Comparing with y√6:

y = −4

Tip: In surd questions like this, break every number into (perfect square) × (the common surd). Look for 4, 9, 16, 25, 36, 100 as factors. Once all the surds are the same, you can treat √6 like a variable, just as you would combine "2x + 4x − 10x".