Add and Subtract Radicals Practice
ANSWER FOR #1 IS:
5√8
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read above
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.
To practice adding and subtracting radicals, you can follow these steps:
Step 1: Simplify the radicals
If the radicals have the same index (root), you can simplify them before adding or subtracting. For example, √8 can be simplified to 2√2.
Step 2: Check if the radicals are like terms
Like terms refer to radicals with the same radicand (the number within the radical symbol). For example, √2 and √2 are like terms because they both have a radicand of 2. On the other hand, √2 and √3 would not be like terms.
Step 3: Add or Subtract the coefficients
Take the coefficients (numbers outside the radical sign) of the like terms, and perform the addition or subtraction on them. For example, if you have 2√2 + 3√2, you can add the coefficients to get 5√2.
Note: If the radicals are not like terms, you cannot directly add or subtract them. You can leave the expression as it is or simplify further if possible.
Here are a few practice problems:
1. √7 + √7
Since the radicals have the same index and radicand, they are like terms. The coefficients are both 1. Adding the coefficients, we get 2. Therefore, the answer is 2√7.
2. 2√5 - 3√5
Again, the radicals have the same index and radicand, so they are like terms. The coefficients are 2 and -3. Subtracting the coefficients, we get -1. The answer is -√5.
3. 4√3 + 2√2
The radicals in this problem are not like terms since they have different radicands (3 and 2). Therefore, you cannot directly add them. The answer will remain as 4√3 + 2√2.
Remember, practice is essential to improve your skills in adding and subtracting radicals. You can create your own practice problems or find online resources that offer additional examples and exercises for further practice.
Sure! I can help you practice adding and subtracting radicals. Here's a step-by-step guide:
Step 1: Simplify each radical expression, if possible. Simplify the square roots of perfect squares.
Step 2: Identify the radicals that can be combined. Radicals with the same radicand (the number inside the radical symbol) can be combined.
Step 3: Add or subtract the coefficients (the numbers outside the radical symbol) of the radicals that have the same radicand.
Step 4: Keep the radical symbol and the radicand unchanged.
Step 5: Simplify the resulting expression, if needed.
Let's go through an example for practice:
Example: Simplify and combine the following radical expressions: √18 + √8 - √2
Step 1: Simplify the radicands, if possible.
- √18 can be simplified as √(9 × 2), which becomes 3√2.
- √8 can be simplified as √(4 × 2), which becomes 2√2.
- √2 cannot be simplified further.
Step 2: Identify the radicals that can be combined.
- There are two radicals with the radicand 2: 3√2 and 2√2.
Step 3: Add or subtract the coefficients of the radicals.
- The coefficients of the radicals with the radicand 2 are 3 and 2.
- Adding 3√2 and 2√2 gives 5√2.
Step 4: Keep the radical symbol and radicand unchanged.
- The radical symbol (√) and the radicand (2) remain unchanged.
Step 5: Simplify the expression, if needed.
- Since 5√2 is already in simplified form, no further simplification is needed.
The simplified form of the expression √18 + √8 - √2 is 5√2.
I hope this step-by-step guide helps you practice adding and subtracting radicals! Let me know if you have any more questions.
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.
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.
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!