What is 440−−√3+34–√3+532−−√3

Question

?(1 point)
Responses

810−−√3+6+202–√3
8 cube root of 10 plus 6 plus 20 cube root of 2

85–√3+74–√3
8 cube root of 5 plus 7 cube root of 4

85–√3+26
8 cube root of 5 plus 26

85–√3+134–√3

Answer 1

To simplify the expression \( 440−−√3 + 34−−√3 + 532−−√3 \), we first rewrite it using square roots:

\[ 440\sqrt{3} + 34\sqrt{3} + 532\sqrt{3}. \]

Now, combine the coefficients of \(\sqrt{3}\):

\[ (440 + 34 + 532)\sqrt{3} = 1006\sqrt{3}. \]

Now let's analyze the provided responses to match the simplified result:

1. \(810−−√3 + 6 + 202−−√3\)
2. \(8 \sqrt[3]{10} + 6 + 20 \sqrt[3]{2}\)
3. \(85−−√3 + 74−−√3\)
4. \(85−−√3 + 26\)
5. \(85−−√3 + 134−−√3\)

Notice that none of these options simplify to \(1006\sqrt{3}\).

Additionally, it seems \( 85\sqrt{3} + 134\sqrt{3} = 219\sqrt{3} \) which doesn't match our result.

None of these responses are equivalent to \( 1006\sqrt{3} \). Please verify the original expression for clarity, or check for any misinterpretation.