Add 321−−√ + 721−−√.(1 point) Responses 1042−−√ 10 Start Root 42 End Root 52−−√ Start Root 52 End Root 1021−−√ 10 Start Root 21 End Root 24 −−−√ + 28−−√ Start Root 24 End Root plus Start Root 28 End Root
1. 10√21
2. 2√`19
3. 3√22 plus 4√22 (sorry i couldnt find the right symbol)
4. 7√23
5. 2√6
tell me if you need the answers for the practice too
ciocolatto is 100% correct, thanks! (2023 connexus)
I need help w/ the quick check
\(321- \sqrt{721} + \sqrt{42} + \sqrt{52} - \sqrt{1021} + \sqrt{21} - \sqrt{24} + \sqrt{28}\)
what?
To add √321 + √721, we need to simplify each square root individually and then add them together.
Step 1: Simplify √321
To find the square root of 321, we can break it down into its prime factors: 3 × 107.
Since there are no perfect squares among these factors, we cannot simplify it further.
Hence, we leave it as √321.
Step 2: Simplify √721
To find the square root of 721, we can break it down into its prime factors: 7 × 103.
Again, there are no perfect squares among these factors, so we cannot simplify it further.
Thus, we leave it as √721.
Now we add the two square roots together:
√321 + √721 = √321 + √721.
So the sum of √321 + √721 cannot be simplified further.
To simplify the expression 321√ + 721√, you can follow these steps:
Step 1: Simplify each radical separately.
- The square root of 321 can be simplified as √321 = √(107*3) = √107 * √3. Since √107 is an irrational number, we cannot simplify it further.
- The square root of 721 can be simplified as √721 = √(103*7) = √103 * √7. Again, since √103 is an irrational number, we cannot simplify it further.
Step 2: Combine like terms.
Since there are no like terms in this expression, we cannot further simplify the sum of the radicals.
Therefore, the final result of 321√ + 721√ is √321 + √721.
Apologies for the confusion. Let's simplify the expression step by step.
We are given:
\(321 - \sqrt{721} + \sqrt{42} + \sqrt{52} - \sqrt{1021} + \sqrt{21} - \sqrt{24} + \sqrt{28}\)
Using a calculator or simplifying each term separately:
\(321 \approx 321\)
\(\sqrt{721} \approx 26.863\)
\(\sqrt{42} \approx 6.481\)
\(\sqrt{52} \approx 7.211\)
\(\sqrt{1021} \approx 31.953\)
\(\sqrt{21} \approx 4.583\)
\(\sqrt{24} \approx 4.899\)
\(\sqrt{28} \approx 5.292\)
Now we can substitute the approximated values into the expression:
\(321 - 26.863 + 6.481 + 7.211 - 31.953 + 4.583 - 4.899 + 5.292\)
Adding and subtracting the terms:
\(= (321) - (26.863) + (6.481 + 7.211 - 31.953 + 4.583 - 4.899 + 5.292)\)
\(= 321 - 26.863 + (-8.513)\)
\(= 294.137 - 8.513\)
\(= 285.624\)
Therefore, the simplified result is approximately 285.624.