Sure, here's a practice problem for adding and subtracting radicals:
Simplify the following expression: √18 + √8 - √2
Solution:
Before we can add or subtract the radicals, we need to simplify them individually.
√18 can be simplified by factoring out the perfect square 9:
√18 = √(9 * 2) = √9 * √2 = 3√2
√8 can be simplified by factoring out the perfect square 4:
√8 = √(4 * 2) = √4 * √2 = 2√2
Now we can substitute the simplified radicals back into the original expression:
3√2 + 2√2 - √2
Since all three terms have the same radical (√2), we can combine like terms:
(3 + 2 - 1)√2 = 4√2
So the simplified expression is 4√2.
Add and Subtract Radicals Practice
21 answers
2√8 + 3√8
To add 2√8 and 3√8, follow these steps:
Step 1: Simplify the radicals, if possible.
√8 can be simplified by factoring out the perfect square 4:
√8 = √(4 * 2) = √4 * √2 = 2√2
Step 2: Check if the radicals are like terms.
Both terms have the same radicand (2√2), so they are like terms.
Step 3: Add the coefficients.
Adding the coefficients of the like terms:
2√2 + 3√2 = (2 + 3)√2 = 5√2
So the final answer is 5√2.
Step 1: Simplify the radicals, if possible.
√8 can be simplified by factoring out the perfect square 4:
√8 = √(4 * 2) = √4 * √2 = 2√2
Step 2: Check if the radicals are like terms.
Both terms have the same radicand (2√2), so they are like terms.
Step 3: Add the coefficients.
Adding the coefficients of the like terms:
2√2 + 3√2 = (2 + 3)√2 = 5√2
So the final answer is 5√2.
wrong
I apologize for the mistake. Let's solve the problem correctly.
To add 2√8 and 3√8, follow these steps:
Step 1: Simplify the radicals, if possible.
√8 can be simplified as √(4 × 2), which becomes 2√2.
Step 2: Check if the radicals are like terms.
Both terms have the same radicand (2√2), so they are like terms.
Step 3: Add the coefficients.
Adding the coefficients of the like terms:
2√2 + 3√2 = (2 + 3)√2 = 5√2
So the correct answer is 5√2.
Thank you for pointing out the mistake, and I apologize for any confusion caused. Let me know if you have any more questions or need further assistance.
To add 2√8 and 3√8, follow these steps:
Step 1: Simplify the radicals, if possible.
√8 can be simplified as √(4 × 2), which becomes 2√2.
Step 2: Check if the radicals are like terms.
Both terms have the same radicand (2√2), so they are like terms.
Step 3: Add the coefficients.
Adding the coefficients of the like terms:
2√2 + 3√2 = (2 + 3)√2 = 5√2
So the correct answer is 5√2.
Thank you for pointing out the mistake, and I apologize for any confusion caused. Let me know if you have any more questions or need further assistance.
try another way
Sure, let's try another approach.
To add 2√8 and 3√8, we can treat √8 as a common factor and add the coefficients:
2√8 + 3√8 = (2 + 3)√8
Now, let's simplify the radicand:
√8 = √(4 * 2) = √4 * √2 = 2√2
Substituting this back into our expression:
(2 + 3)√8 = 5√2
So the answer is 5√2.
I hope this clears up any confusion. Again, I apologize for the earlier mistake. Let me know if you have any more questions!
To add 2√8 and 3√8, we can treat √8 as a common factor and add the coefficients:
2√8 + 3√8 = (2 + 3)√8
Now, let's simplify the radicand:
√8 = √(4 * 2) = √4 * √2 = 2√2
Substituting this back into our expression:
(2 + 3)√8 = 5√2
So the answer is 5√2.
I hope this clears up any confusion. Again, I apologize for the earlier mistake. Let me know if you have any more questions!
it still wrong please try a different answer
Apologies for the confusion earlier. Let's try a different approach to correctly solve the problem.
To add 2√8 and 3√8, we can rewrite the radicals using the same radicand:
2√8 + 3√8 = (2 + 3)√8
Next, let's simplify the radicand:
√8 = √(4 * 2) = √4 * √2 = 2√2
Substituting this back into our expression:
(2 + 3)√8 = 5√8
However, we can simplify further by factoring out the common factor:
5√8 = 5√(4 * 2) = 5√4 * √2 = 5*2√2 = 10√2
So the correct answer is 10√2.
I apologize for any confusion caused and I appreciate your patience. Let me know if you have any further questions!
To add 2√8 and 3√8, we can rewrite the radicals using the same radicand:
2√8 + 3√8 = (2 + 3)√8
Next, let's simplify the radicand:
√8 = √(4 * 2) = √4 * √2 = 2√2
Substituting this back into our expression:
(2 + 3)√8 = 5√8
However, we can simplify further by factoring out the common factor:
5√8 = 5√(4 * 2) = 5√4 * √2 = 5*2√2 = 10√2
So the correct answer is 10√2.
I apologize for any confusion caused and I appreciate your patience. Let me know if you have any further questions!
√31+√31
To add √31 and √31, we can simply combine the coefficients since the radicals have the same radicands:
√31 + √31 = (1 + 1)√31 = 2√31
So the sum of √31 and √31 is 2√31.
Let me know if you have any more questions!
√31 + √31 = (1 + 1)√31 = 2√31
So the sum of √31 and √31 is 2√31.
Let me know if you have any more questions!
7√5-4√57
To subtract 4√57 from 7√5, follow these steps:
Step 1: Simplify the radicals, if possible.
√57 cannot be simplified any further.
Step 2: Check if the radicals are like terms.
Both terms do not have the same radicand (5 and 57), so they are not like terms.
Step 3: Subtract the coefficients.
Subtracting the coefficients of the terms:
7√5 - 4√57
Step 4: Keep the radical symbol and radicand unchanged.
The radical symbol (√) and the radicands (5 and 57) remain unchanged.
So the final answer is 7√5 - 4√57.
Please let me know if you have any further questions or need more assistance!
Step 1: Simplify the radicals, if possible.
√57 cannot be simplified any further.
Step 2: Check if the radicals are like terms.
Both terms do not have the same radicand (5 and 57), so they are not like terms.
Step 3: Subtract the coefficients.
Subtracting the coefficients of the terms:
7√5 - 4√57
Step 4: Keep the radical symbol and radicand unchanged.
The radical symbol (√) and the radicands (5 and 57) remain unchanged.
So the final answer is 7√5 - 4√57.
Please let me know if you have any further questions or need more assistance!
7√5 - 4√5
To subtract 4√5 from 7√5, follow these steps:
Step 1: Simplify the radicals, if possible.
Both terms have the same radicand, which is 5.
Step 2: Check if the radicals are like terms.
Since both terms have the same radicand, they are like terms.
Step 3: Subtract the coefficients.
Subtracting the coefficients of the terms:
7√5 - 4√5 = (7 - 4)√5 = 3√5
So the final answer is 3√5.
Please let me know if there's anything else I can help you with!
Step 1: Simplify the radicals, if possible.
Both terms have the same radicand, which is 5.
Step 2: Check if the radicals are like terms.
Since both terms have the same radicand, they are like terms.
Step 3: Subtract the coefficients.
Subtracting the coefficients of the terms:
7√5 - 4√5 = (7 - 4)√5 = 3√5
So the final answer is 3√5.
Please let me know if there's anything else I can help you with!
√29-√29
To subtract √29 from √29, follow these steps:
Step 1: Simplify the radicals, if possible.
Both terms have the same radicand, which is 29.
Step 2: Check if the radicals are like terms.
Since both terms have the same radicand, they are like terms.
Step 3: Subtract the coefficients.
Subtracting the coefficients of the terms:
√29 - √29 = (1 - 1)√29 = 0√29
So the final answer is 0√29, which simplifies to 0.
Therefore, √29 - √29 equals 0.
If you have any more questions, feel free to ask!
Step 1: Simplify the radicals, if possible.
Both terms have the same radicand, which is 29.
Step 2: Check if the radicals are like terms.
Since both terms have the same radicand, they are like terms.
Step 3: Subtract the coefficients.
Subtracting the coefficients of the terms:
√29 - √29 = (1 - 1)√29 = 0√29
So the final answer is 0√29, which simplifies to 0.
Therefore, √29 - √29 equals 0.
If you have any more questions, feel free to ask!
ANSWER FOR #1 IS:
5√8
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read above
5√8
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read above
I apologize for the confusion. Let's correctly solve the problem.
To add 2√8 and 3√8, follow these steps:
Step 1: Simplify the radicals, if possible.
√8 can be simplified as √(4 × 2), which becomes 2√2.
Step 2: Check if the radicals are like terms.
Both terms have the same radicand (2√2), so they are like terms.
Step 3: Add the coefficients.
Adding the coefficients of the like terms:
2√2 + 3√2 = (2 + 3)√2 = 5√2
So the correct answer is 5√2.
Thank you for pointing out the mistake, and I apologize for any confusion caused. Let me know if you have any more questions or need further assistance.
To add 2√8 and 3√8, follow these steps:
Step 1: Simplify the radicals, if possible.
√8 can be simplified as √(4 × 2), which becomes 2√2.
Step 2: Check if the radicals are like terms.
Both terms have the same radicand (2√2), so they are like terms.
Step 3: Add the coefficients.
Adding the coefficients of the like terms:
2√2 + 3√2 = (2 + 3)√2 = 5√2
So the correct answer is 5√2.
Thank you for pointing out the mistake, and I apologize for any confusion caused. Let me know if you have any more questions or need further assistance.
The tiles in a store are being compared. The diagonal of one tile is 9√2 centimeters, and the other tile is 8√2 centimeters. What is the difference in the length of the diagonals?
The difference is...
The difference is...
To find the difference in the length of the diagonals, we subtract the length of one diagonal from the other.
The length of the first diagonal is 9√2 centimeters.
The length of the second diagonal is 8√2 centimeters.
To find the difference, we subtract the second diagonal from the first:
(9√2) - (8√2) = 9√2 - 8√2
Since the radicands are the same, we can subtract the coefficients:
(9 - 8)√2 = 1√2
Simplifying further, we find that √2 cannot be simplified any further.
Therefore, the difference in the length of the diagonals is 1√2 centimeters.
The length of the first diagonal is 9√2 centimeters.
The length of the second diagonal is 8√2 centimeters.
To find the difference, we subtract the second diagonal from the first:
(9√2) - (8√2) = 9√2 - 8√2
Since the radicands are the same, we can subtract the coefficients:
(9 - 8)√2 = 1√2
Simplifying further, we find that √2 cannot be simplified any further.
Therefore, the difference in the length of the diagonals is 1√2 centimeters.
1 answer