If $\sqrt{72} + \sqrt{32} - 3 \sqrt{18} = x \sqrt{8}$, Find the value of x

Analyze the question: We need to simplify each surd, combine like terms, and express the result as a multiple of √8.

Concept: Simplify a surd by pulling out perfect squares: √(a²b) = a√b. Surds with the same radical can be added or subtracted like like terms.

Solution:

• √72 = √(36 × 2) = 6√2
• √32 = √(16 × 2) = 4√2
• 3√18 = 3√(9 × 2) = 3 × 3√2 = 9√2

Left side: 6√2 + 4√2 − 9√2 = (6 + 4 − 9)√2 = √2

Right side: x√8 = x√(4 × 2) = 2x√2

Equate: √2 = 2x√2 1 = 2x x = 1/2

Answer: x = 1/2, which is option C.

Tip: Always break surds into a perfect square times the smallest remaining number (here, 2). Once everything is in terms of √2, the arithmetic becomes simple. Also remember √8 = 2√2 to convert the right side quickly.