Simplify $\sqrt{6a^{-2}} \times \sqrt{24a^6}$

Step 1: Analyze the question We need to multiply two square roots and simplify. The expressions inside are 6a⁻² and 24a⁶.

Step 2: Concept √x × √y = √(xy), and when we take a square root, the result is ± (positive or negative).

Step 3: Solution

Combine under one root:

√(6a⁻²) × √(24a⁶) = √(6 × 24 × a⁻² × a⁶)

• 6 × 24 = 144
• a⁻² × a⁶ = a^(−2+6) = a⁴

So we have:

√(144a⁴) = ±12a²

(Since √144 = 12 and √(a⁴) = a².)

Step 4: Answer The result is ±12a², which is option D.

Tip: When multiplying roots, combine them first, then multiply the numbers and add the powers of the same base. Halve the index at the end to take the square root (a⁴ → a²). Don't forget the ± sign when the question uses it in the options!