Which expression simplifies to 65–√3

Question

?(1 point)
Responses

440−−√3−25–√3
4 cube root of 40 minus 2 cube root of 5

340−−√3+35–√3
3 cube root of 40 plus 3 cube root of 5

23–√3−42–√3
2 cube root of 3 minus 4 cube root of 2

−540−−√3−5–√3

Answer 1

To find the expression that simplifies to \( 65 - \sqrt{3} \), let’s evaluate each option:

1. Option 1: \( \sqrt{440} - 25\sqrt{3} \)

• First, simplify \( \sqrt{440} = \sqrt{4 \cdot 110} = 2\sqrt{110} \).
• Therefore, this expression becomes \( 2\sqrt{110} - 25\sqrt{3} \), which does not simplify to \( 65 - \sqrt{3} \).

2. Option 2: \( 3\sqrt[3]{40} + 3\sqrt[3]{5} \)

• This does not directly translate to \( 65 - \sqrt{3} \) and seems unrelated.

3. Option 3: \( 2\sqrt{3} - 4\sqrt{2} \)

• This again does not simplify to \( 65 - \sqrt{3} \).

4. Option 4: \( -5\sqrt{40} - 5\sqrt{3} \)

• Simplifying \( \sqrt{40} = \sqrt{4 \cdot 10} = 2\sqrt{10} \),
• Thus, this expression becomes \( -5(2\sqrt{10}) - 5\sqrt{3} = -10\sqrt{10} - 5\sqrt{3} \), which is also not \( 65 - \sqrt{3} \).

None of the provided options directly simplify to \( 65 - \sqrt{3} \). However, if there are any additional corrections or clarifications regarding the problem, please provide them for further assistance.