Which expression simplifies to 65–√3

Question

6
5
3
?(1 point)
Responses
440−−√3−25–√3
4
40
3
−
2
5
3
4 cube root of 40 minus 2 cube root of 5
23–√3−42–√3
2
3
3
−
4
2
3
2 cube root of 3 minus 4 cube root of 2
340−−√3+35–√3
3
40
3
+
3
5
3
3 cube root of 40 plus 3 cube root of 5
−540−−√3−5–√3

Answer 1

To find which expression simplifies to \( 65 - \sqrt{3} \), we will analyze each of the responses given:

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

   Simplifying \( \sqrt{440} \):

   \[ \sqrt{440} = \sqrt{4 \cdot 110} = 2\sqrt{110} \]

   This response simplifies to \( 2\sqrt{110} - 25 - \sqrt{3} \), which does not simplify to \( 65 - \sqrt{3} \).

2. Response 2: \( 4 \sqrt[3]{40} - 2 \sqrt[3]{5} \)

   This is more complex and involves cube roots. We cannot determine easily if this equals \( 65 - \sqrt{3} \) without specific values for the cube roots.

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

   This again has square roots and does not simplify to \( 65 - \sqrt{3} \).

4. Response 4: \( 3 \sqrt[3]{40} + 3 \sqrt[3]{5} \)

   Similar to the other cube root expressions that would likely not simplify.

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

   Simplifying \( -5 \sqrt{40} \):

   \[ -5 \sqrt{40} = -5 \cdot 2 \sqrt{10} = -10 \sqrt{10} \]

   This results in \( -10 \sqrt{10} - 5\sqrt{3} \), which does not simplify to \( 65 - \sqrt{3} \).

After reviewing all options, none of the responses given simplistically come to \( 65 - \sqrt{3} \). Thus, it appears none of the responses match the required expression, based on the calculations performed.

If you have the expression that each option simplifies further, I would highly recommend checking each reference with numerical approximations or further context would help clarify.