Question
Add the following radicals. Give the answer in simplest radical form. 43–√+248−−√ (1 point) Responses 126–√ 12 square root of 6 123–√ 12 square root of 3 363–√ 36 square root of 3 651−−√
Answers
GPT-4o mini
To add the radicals \( \sqrt{43} + \sqrt{248} \), we first simplify \( \sqrt{248} \).
1. **Simplifying \( \sqrt{248} \)**:
- The prime factorization of \( 248 \) is \( 2^3 \times 31 \).
- We can separate the perfect square:
\[
\sqrt{248} = \sqrt{4 \times 62} = \sqrt{4} \sqrt{62} = 2\sqrt{62}
\]
2. **Now adding \( \sqrt{43} + 2\sqrt{62} \)**:
- These radicals cannot be combined further because \( \sqrt{43} \) and \( \sqrt{62} \) are not like terms.
Thus, the final answer is:
\[
\sqrt{43} + 2\sqrt{62}
\]
None of the response options provided match this answer directly. However, the correctly simplified radical expression remains \( \sqrt{43} + 2\sqrt{62} \). If there was a typo or misunderstanding in the options, please double-check them. If you need any further clarification or help, do let me know!
1. **Simplifying \( \sqrt{248} \)**:
- The prime factorization of \( 248 \) is \( 2^3 \times 31 \).
- We can separate the perfect square:
\[
\sqrt{248} = \sqrt{4 \times 62} = \sqrt{4} \sqrt{62} = 2\sqrt{62}
\]
2. **Now adding \( \sqrt{43} + 2\sqrt{62} \)**:
- These radicals cannot be combined further because \( \sqrt{43} \) and \( \sqrt{62} \) are not like terms.
Thus, the final answer is:
\[
\sqrt{43} + 2\sqrt{62}
\]
None of the response options provided match this answer directly. However, the correctly simplified radical expression remains \( \sqrt{43} + 2\sqrt{62} \). If there was a typo or misunderstanding in the options, please double-check them. If you need any further clarification or help, do let me know!