Add 22−−√3 + 322−−√ + 22−−√.(1 point)
Responses
566−−√
5 Start Root 66 End Root
522−−√
5 Start Root 22 End Root
22−−√3 + 422−−√
root index 3 Start Root 22 End Root plus 4 Start Root 22 End Root
22−−√3 + 444−−√
root index 3 Start Root 22 End Root plus 4 Start Root 44 End Root
Sorry, I made a mistake in my previous response. The correct answer is:
22−−√3 + 322−−√ + 22−−√ = 5√6 + 5√2 + 2√2 = (5 + 5 + 2)√2 = 12√2
To add 22√3 + 322√ + 22√, we need to simplify each term separately.
First, let's simplify 22√3. Since there is no perfect square that can be extracted from 3, the simplified form of 22√3 remains the same.
Next, let's simplify 322√. Taking the square root of 322, we get √322. However, since 322 does not have any perfect square factors, we cannot simplify it further.
Lastly, let's simplify 22√. Again, there are no perfect square factors in 2, so the simplified form remains the same.
Therefore, the sum of 22√3 + 322√ + 22√ is 22√3 + 322√ + 22√.
To add the given expressions: 22−−√3 + 322−−√ + 22−−√, you cannot directly add the square root terms together. Instead, you need to simplify each term individually and then add them together.
Let's simplify each term:
1. Simplify 22−−√3:
The square root of 22 can be simplified to 2√2, then you raise it to the power of 3, which gives you (2√2)^3 = 2^3 * (√2)^3 = 8√8.
2. Simplify 322−−√:
The square root of 32 can be simplified as √(16 * 2). Since 16 is a perfect square, it can be taken out of the square root, giving you 4√2. Thus, 32−−√ = 4√2.
3. Simplify 22−−√:
The square root of 22 cannot be simplified any further, so it remains as 22−−√.
Now, add these simplified terms together:
8√8 + 4√2 + 22−−√
Since the terms with square roots are different, you cannot directly combine them. So, the answer would be:
8√8 + 4√2 + 22−−√