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Question

Question
Simplify the expression 64 −−−−√3 + 3(22+5−−−−−√ )
(1 point)
Responses

13
13

17
17

21
21

31

Answer 1

To simplify the expression \( \sqrt[3]{64} + 3(22 + \sqrt{5}) \), let's break it down step by step.

1. Calculate \( \sqrt[3]{64} \): \[ \sqrt[3]{64} = 4 \quad (\text{since } 4 \times 4 \times 4 = 64) \]

2. Calculate the expression inside the parentheses: \[ 22 + \sqrt{5} \quad (\text{leave this as it is for now}) \]

3. Multiply by 3: \[ 3(22 + \sqrt{5}) = 3 \times 22 + 3 \times \sqrt{5} = 66 + 3\sqrt{5} \]

4. Combine everything: \[ \sqrt[3]{64} + 3(22 + \sqrt{5}) = 4 + 66 + 3\sqrt{5} = 70 + 3\sqrt{5} \]

Since \( 3\sqrt{5} \) is not a whole number, it can't be simplified further into one of the options given. Therefore, the expression simplifies to \( 70 + 3\sqrt{5} \).

However, none of the options (13, 17, 21, 31) match this result. It appears we may have a miscommunication on the expression intended for simplification or there’s an issue with the provided choices.

If you prefer to select from the options you've provided without correct calculations, please clarify or share the expression again for accurate results.

Answer 2

wrong

Answer 3

I apologize for the confusion in my previous response. Let's clarify the original expression and simplify it step by step again.

The expression given is:

\[ \sqrt[3]{64} - 3(22+\sqrt{5}) \]

Let's simplify it correctly:

1. Calculate \( \sqrt[3]{64} \): \[ \sqrt[3]{64} = 4 \]

2. Now simplify \( 3(22+\sqrt{5}) \): \[ 3(22+\sqrt{5}) = 3 \times 22 + 3 \times \sqrt{5} = 66 + 3\sqrt{5} \]

3. Now combine the terms: \[ 4 - (66 + 3\sqrt{5}) = 4 - 66 - 3\sqrt{5} = -62 - 3\sqrt{5} \]

This doesn't directly give a whole number or match any of the choices (13, 17, 21, 31), indicating a possible misunderstanding of the expression or values.

If we assume you meant:

If the expression was intended to be:

\[ \sqrt{64} - 3(22+\sqrt{5}) \]

Then we would do:

1. Calculate \( \sqrt{64} \): \[ \sqrt{64} = 8 \]

2. Multiply out \( 3(22+\sqrt{5}) \): \[ 3(22+\sqrt{5}) = 66 + 3\sqrt{5} \]

3. Combine the terms: \[ 8 - (66 + 3\sqrt{5}) = 8 - 66 - 3\sqrt{5} = -58 - 3\sqrt{5} \]

But again, this results in something not matching your options.

Correcting the Assumption:

Could you please confirm the original expression? If it was supposed to be \( \sqrt[3]{64} + 3(22+\sqrt{5}) \) or included other operations, that might have changed everything.

Let’s clarify your question so I can provide the correct simplification!