Add 22−−√3 + 322−−√ + 22−−√.(1 point) Responses 522−−√ 5 Start Root 22 End Root 566−−√ 5 Start Root 66 End Root 22−−√3 + 444−−√ root index 3 Start Root 22 End Root plus 4 Start Root 44 End Root 22−−√3 + 422−−√
To add these numbers, we need to simplify each radical first:
22−−√3 = √3
322−−√ = √32
22−−√ = √2
Now we can add them:
√3 + √32 + √2
We cannot simplify this further, so our final answer is:
√3 + √32 + √2
To solve the expression 22−√3 + 322−√ + 22−√, follow these steps:
Step 1: Simplify the square roots separately:
- √3 is already simplified.
- √3 = √3
- √32 = √9 = 3
- √2 = √2
Step 2: Add the simplified square roots:
- √3 + 3 + √2
Step 3: Combine like terms:
- √3 + √2 + 3
Therefore, the simplified expression is √3 + √2 + 3.
To add the expression 22√3 + 322√ + 22√, you need to simplify each part separately and then combine them.
1. Simplify 22√3:
- The square root of 3 (√3) cannot be simplified further, so it remains as √3.
- Therefore, 22√3 remains as 22√3.
2. Simplify 322√:
- The square root of 2 (√2) cannot be simplified further, so it remains as √2.
- Therefore, 322√ becomes 32√2.
3. Simplify 22√:
- The square root of 2 (√2) cannot be simplified further, so it remains as √2.
- Therefore, 22√ becomes 2√2.
Now, you can add the simplified parts together:
22√3 + 32√2 + 2√2.
To combine like terms, you add the coefficients that share the same radical term:
22√3 + (32 + 2)√2.
Simplifying further:
22√3 + 34√2.
The final answer is 22√3 + 34√2.