1Add 321−−√ + 721−−√ . 52−−√ Start Root 52 End Root 24 −−−√ + 28−−√ Start Root 24 End Root plus Start Root 28 End Root 1042−−√ 10 Start Root 42 End Root 1021−−√
2Add 19−−√ + 19−−√. 20−−√ Start Root 20 End Root 219−−√ 2 Start Root 19 End Root 238−−√ 2 Start Root 38 End Root 40−−√ Start Root 40 End Root
3 Add 22−−√3 + 322−−√ + 22−−√.(1 point) Responses 22−−√3 + 444−−√ root index 3 Start Root 22 End Root plus 4 Start Root 44 End Root 22−−√3 + 422−−√ root index 3 Start Root 22 End Root plus 4 Start Root 22 End Root 566−−√ 5 Start Root 66 End Root 522−−√
4 Subtract 823−−√−23−−√. (1 point) Responses 846−−√ 8 start root 46 end root 746−−√ 7 start root 46 end root 723−−√ 7 start root 23 end root 823−−√
5Jake runs 76–√ miles on Monday and 56–√ miles on Tuesday. What is the difference in miles run each day?(1 point) Responses 26–√ 2 start root 6 end root 212−−√ 2 start root 12 end root 412−−√ 4 start root 12 end root 46–√
The difference in miles run each day is 20–√ miles.
1) To add √321 + √721 + √52 - √24 + √28 - √1042 + √10 - √42:
Step 1: Simplify each individual square root:
√321 = √(17 * 19) = √17 * √19
√721 = √(7 * 103) = √7 * √103
√52 = 2√13
√24 = 2√6
√28 = 2√7
√1042 = √(2 * 521) = √2 * √521
√10 = √(2 * 5) = √2 * √5
√42 = √(2 * 3 * 7) = √2 * √3 * √7
Step 2: Group the like terms:
(√17 + √7) + (√19 + √103) + 2√13 - 2√6 + 2√7 - √2 * √521 + √2 * √5 - √2 * √3 * √7
Step 3: Combine like terms:
√17 + √7 + √19 + √103 + 2√13 - 2√6 + 2√7 - √2√521 + √2√5 - √2√3√7
2) To add √19 + √19 + √20:
Step 1: Simplify each individual square root:
√19 + √19 = 2√19
√20 = 2√5
Step 2: Combine like terms:
2√19 + 2√5
3) To add √22^3 + √322 + √22:
Step 1: Simplify each individual square root:
√22^3 = 2√22
√322 = √(2 * 161) = √2 * √161
√22 = 2√22
Step 2: Combine like terms:
2√22 + √2√161 + 2√22
4) To subtract √823 - √23:
Step 1: Simplify each individual square root:
√823 = √(17 * 7 * 7) = √(17 * 7^2) = √17 * 7
√23 = √(23) = √23
Step 2: Subtract the two square roots:
√17 * 7 - √23
5) To find the difference between √76 and √56:
Step 1: Simplify each individual square root:
√76 = √(4 * 19) = √4 * √19 = 2√19
√56 = √(2 * 2 * 14) = √(2^2 * 14) = 2√14
Step 2: Subtract the two square roots:
2√19 - 2√14
To solve these questions involving square roots, you can follow these steps:
1. Add or subtract the numbers inside the square roots separately.
2. Simplify each square root expression if possible.
3. Perform the addition or subtraction operation on the simplified square root expressions.
4. If needed, simplify the result further by finding the square root.
Let's apply these steps to the given questions:
1. Add √321 + √721 + √52. Subtract √24 + √28.
- Simplify each square root expression:
√321 = √(107^2) = 107
√721 = √(107^2 + 4) = √(107^2) + √(2^2) = 107 + 2 = 109
√52 = √(25) = 5
√24 = √(4^2 * 3) = 2√3
√28 = √(4^2 * 7) = 2√7
- Perform addition: 107 + 109 + 5 - 2√3 + 2√7
- Simplify if possible: 221 + 2√7 - 2√3
Therefore, the result is 221 + 2√7 - 2√3.
2. Add √19 + √19.
- Simplify each square root expression:
√19 + √19 = 2√19
Therefore, the result is 2√19.
3. Add √3 + √32 + √22.
- Simplify each square root expression:
√3 = √(3) = √(3)
√32 = √(2^3 * 2) = 2√2
√22 = √(2^2 * 11) = 2√11
- Perform addition: √3 + 2√2 + 2√11
- Simplify if possible: √3 + 2√2 + 2√11
Therefore, the result is √3 + 2√2 + 2√11.
4. Subtract √823 - √23.
- Simplify each square root expression:
√823 = √(29^2) = 29
√23 = √(23) = √(23)
- Perform subtraction: 29 - √23
- Simplify if possible: 29 - √23
Therefore, the result is 29 - √23.
5. Find the difference between √76 and √56.
- Simplify each square root expression:
√76 = √(4^2 * 19) = 4√19
√56 = √(2^3 * 7) = 2√14
- Perform subtraction: 4√19 - 2√14
- Simplify if possible: 4√19 - 2√14
Therefore, the result is 4√19 - 2√14.
Remember to always simplify and combine like terms whenever possible.