Simplify:($\frac{10\sqrt{3}}{\sqrt{5}} - \sqrt{15}$)2

The "2" at the end is unclear. It could mean squaring the bracket, or it could be a typo. Let's work it out.

Step 1: Simplify the expression inside the bracket

10√3/√5 = 10√3·√5/5 = 2√15

So the bracket becomes: 2√15 − √15 = √15

Step 2: Apply the "2"

• If it means squared: (√15)² = 15
• If it means divided by 2: √15 / 2 ≈ 1.94, which is not an option.
• If it means multiplied by 2: 2√15 ≈ 7.75, which is not an option.

Only the "squared" reading matches an option, and it gives 15.

Check the other options:

• 75 would come from wrongly squaring only the first term, (10√3/√5)² = 100·3/5 = 60, and then making further errors.
• 8.66 is 5√3, and 3.87 is √15. These come from incorrect simplification or from forgetting to square.

Answer: B (15)

Tip: When you see a fraction with a surd in the denominator, rationalise it first (multiply the top and bottom by that surd). That often reveals like terms, such as 2√15 − √15, that combine easily.