Evaluate: 2$\sqrt{28} - 3\sqrt{50} + \sqrt{72}$

Step 1: Analyze the question We need to simplify each surd by pulling out perfect squares, then combine like terms.

Step 2: Concept √(a²b) = a√b. Only surds with the same radicand (like √7 with √7, √2 with √2) can be added or subtracted.

Step 3: Solution

• 2√28 = 2√(4 × 7) = 2 × 2√7 = 4√7
• 3√50 = 3√(25 × 2) = 3 × 5√2 = 15√2
• √72 = √(36 × 2) = 6√2

Now combine:

4√7 − 15√2 + 6√2 = 4√7 − 9√2

Step 4: Answer The result is 4√7 − 9√2, which matches option C.

Tip: Always break each surd using the largest perfect square factor (4, 9, 16, 25, 36, 49...). For example, 50 = 25 × 2 and 72 = 36 × 2. Then group the √2 terms together and the √7 terms together. Be careful with signs: −15 + 6 = −9, not −21 or −11.