Asked by x
What is the sum of 513−−√+13−−√+213−−√ ?(1 point)
Responses
839−−√
8 square root of 39
47−−√
square root of 47
813−−√
8 square root of 13
713−−√
give the closest possible answer
Responses
839−−√
8 square root of 39
47−−√
square root of 47
813−−√
8 square root of 13
713−−√
give the closest possible answer
Answers
Answered by
x
Add the following radicals. Give the answer in simplest radical form.
43–√+248−−√
(1 point)
Responses
651−−√
6 square root of 51
126–√
12 square root of 6
123–√
12 square root of 3
363–√
give the closest answer possible
43–√+248−−√
(1 point)
Responses
651−−√
6 square root of 51
126–√
12 square root of 6
123–√
12 square root of 3
363–√
give the closest answer possible
Answered by
x
Question
What is the difference of 325–√−175–√ ?(1 point)
Responses
The radicals cannot be combined using subtraction.
The radicals cannot be combined using subtraction.
155–√
15 square root of 5
150–√
15 square root of 0
495–√
give the closest possible answer, no explanation
What is the difference of 325–√−175–√ ?(1 point)
Responses
The radicals cannot be combined using subtraction.
The radicals cannot be combined using subtraction.
155–√
15 square root of 5
150–√
15 square root of 0
495–√
give the closest possible answer, no explanation
Answered by
x
What is the difference of 8125−−−√−780−−√ ?(1 point)
Responses
35–√
3 square root of 5
885–√
88 square root of 5
125–√
12 square root of 5
2110−−−√
give the closest possible answer, no explanation
Responses
35–√
3 square root of 5
885–√
88 square root of 5
125–√
12 square root of 5
2110−−−√
give the closest possible answer, no explanation
Answered by
x
Combine the radicals using addition and subtraction, if possible.
924−−√−56–√+354−−√ ?
(1 point)
Responses
226–√
22 square root of 6
46–√
4 square root of 6
Unlike radicals cannot be combined using addition and subtraction.
Unlike radicals cannot be combined using addition and subtraction.
422–√
42 square root of 2
give the closest answer possible, no explanation
924−−√−56–√+354−−√ ?
(1 point)
Responses
226–√
22 square root of 6
46–√
4 square root of 6
Unlike radicals cannot be combined using addition and subtraction.
Unlike radicals cannot be combined using addition and subtraction.
422–√
42 square root of 2
give the closest answer possible, no explanation
Answered by
GPT-4o mini
To find the sum \( \sqrt{513} + \sqrt{13} + \sqrt{213} \), we first simplify the square roots as much as possible.
1. Notice that:
- \( \sqrt{513} \): This can be simplified since \( 513 = 3^3 \times 19 \), so \( \sqrt{513} = 3\sqrt{57} \) (not a perfect simplification).
- \( \sqrt{13} \) is already in its simplest form.
- \( \sqrt{213} \): This can also be simplified since \( 213 = 3 \times 71 \), making \( \sqrt{213} = \sqrt{3} \sqrt{71} \) (not a perfect simplification).
2. Then, we try to combine these expressions:
\[
\sqrt{513} + \sqrt{13} + \sqrt{213} = \sqrt{513} + \sqrt{213} + \sqrt{13}
\]
3. To provide a contextual value, let's approximate each term:
- \( \sqrt{513} \approx 22.65 \)
- \( \sqrt{13} \approx 3.61 \)
- \( \sqrt{213} \approx 14.59 \)
4. Now, sum these approximations:
\[
22.65 + 3.61 + 14.59 \approx 40.85
\]
5. Since \( \sqrt{39} \) is around \( 6.24 \), the option \( 8\sqrt{39} \) is approximately \( 49.92 \), which is too high.
6. Calculating \( 47^{1/2} \) gives roughly \( 6.86 \), and \( \sqrt{13} \) would not combine additively.
7. Comparing \( \sqrt{3(213} \approx 14.59 \): That means \( 8 \sqrt{13} \approx 22.29 \) similarly falls short.
Therefore, the closest possible answer to \( \sqrt{513} + \sqrt{13} + \sqrt{213} \) is likely \( \sqrt{47} \), though not perfect.
The final and round answer, given your options and closest possible number, is:
**Square root of 47**.
1. Notice that:
- \( \sqrt{513} \): This can be simplified since \( 513 = 3^3 \times 19 \), so \( \sqrt{513} = 3\sqrt{57} \) (not a perfect simplification).
- \( \sqrt{13} \) is already in its simplest form.
- \( \sqrt{213} \): This can also be simplified since \( 213 = 3 \times 71 \), making \( \sqrt{213} = \sqrt{3} \sqrt{71} \) (not a perfect simplification).
2. Then, we try to combine these expressions:
\[
\sqrt{513} + \sqrt{13} + \sqrt{213} = \sqrt{513} + \sqrt{213} + \sqrt{13}
\]
3. To provide a contextual value, let's approximate each term:
- \( \sqrt{513} \approx 22.65 \)
- \( \sqrt{13} \approx 3.61 \)
- \( \sqrt{213} \approx 14.59 \)
4. Now, sum these approximations:
\[
22.65 + 3.61 + 14.59 \approx 40.85
\]
5. Since \( \sqrt{39} \) is around \( 6.24 \), the option \( 8\sqrt{39} \) is approximately \( 49.92 \), which is too high.
6. Calculating \( 47^{1/2} \) gives roughly \( 6.86 \), and \( \sqrt{13} \) would not combine additively.
7. Comparing \( \sqrt{3(213} \approx 14.59 \): That means \( 8 \sqrt{13} \approx 22.29 \) similarly falls short.
Therefore, the closest possible answer to \( \sqrt{513} + \sqrt{13} + \sqrt{213} \) is likely \( \sqrt{47} \), though not perfect.
The final and round answer, given your options and closest possible number, is:
**Square root of 47**.
Answered by
GPT-4o mini
To simplify the expression \( \sqrt{43} + 2\sqrt{48} \), we first need to simplify \( \sqrt{48} \).
1. **Simplifying \( \sqrt{48} \):**
\[
\sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3}
\]
2. **Substituting back into the expression:**
\[
\sqrt{43} + 2\sqrt{48} = \sqrt{43} + 2(4\sqrt{3}) = \sqrt{43} + 8\sqrt{3}
\]
3. **Final expression:**
Thus, the final expression in simplest radical form is:
\[
\sqrt{43} + 8\sqrt{3}
\]
Looking at the response options provided:
1. \( \sqrt{651} \)
2. \( 12\sqrt{6} \)
3. \( 12\sqrt{3} \)
4. \( \sqrt{363} \)
None of these options match our result directly. However, we can analyze the expressions to see if there's a close match.
- \( \sqrt{651} \) simplifies to \( \sqrt{3 \cdot 217} \).
- \( \sqrt{363} \) is \( \sqrt{3 \cdot 121} \) or \( 11\sqrt{3} \).
Since \( \sqrt{43} + 8\sqrt{3} \) is likely **closest to \( 12\sqrt{3}\)**, but this isn't a perfect match to our sum.
Thus, if we need to select one, the best resonating option appears to be: **\( 12\sqrt{3} \)**, considering rounding or approximation.
1. **Simplifying \( \sqrt{48} \):**
\[
\sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3}
\]
2. **Substituting back into the expression:**
\[
\sqrt{43} + 2\sqrt{48} = \sqrt{43} + 2(4\sqrt{3}) = \sqrt{43} + 8\sqrt{3}
\]
3. **Final expression:**
Thus, the final expression in simplest radical form is:
\[
\sqrt{43} + 8\sqrt{3}
\]
Looking at the response options provided:
1. \( \sqrt{651} \)
2. \( 12\sqrt{6} \)
3. \( 12\sqrt{3} \)
4. \( \sqrt{363} \)
None of these options match our result directly. However, we can analyze the expressions to see if there's a close match.
- \( \sqrt{651} \) simplifies to \( \sqrt{3 \cdot 217} \).
- \( \sqrt{363} \) is \( \sqrt{3 \cdot 121} \) or \( 11\sqrt{3} \).
Since \( \sqrt{43} + 8\sqrt{3} \) is likely **closest to \( 12\sqrt{3}\)**, but this isn't a perfect match to our sum.
Thus, if we need to select one, the best resonating option appears to be: **\( 12\sqrt{3} \)**, considering rounding or approximation.
Answered by
GPT-4o mini
The closest answer is **15 square root of 5**.
Answered by
GPT-4o mini
The closest answer is **35–√**.
Answered by
GPT-4o mini
The closest answer is **226–√**.