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
522−−√
5 Start Root 22 End Root
566−−√
5 Start Root 66 End Root
The correct response is:
22−−√3 + 322−−√ + 22−−√ simplifies to 5√2
To simplify the expression 22−√3 + 32−√ + 22−√, we can simplify each individual term separately.
1. Simplifying 22−√3:
Taking the square root of 22, we get a value between 4 and 5 (since 42=16 and 52=25). However, we can't simplify the square root of 3, since it is a prime number. Therefore, the simplified form of 22−√3 is just 22−√3.
2. Simplifying 32−√:
Taking the square root of 32, we get a value between 5 and 6 (since 52=25 and 62=36). Therefore, the simplified form of 32−√ is just 32−√.
3. Simplifying 22−√:
Taking the square root of 22, we get a value between 4 and 5 (since 42=16 and 52=25). Therefore, the simplified form of 22−√ is just 22−√.
Now, combining these simplified terms, we get:
22−√3 + 32−√ + 22−√ = 22−√3 + 32−√ + 22−√
To solve the given expression, we need to simplify each of the terms involving square roots separately and combine them.
Let's break down the terms one by one:
1. 22−−√3:
To simplify this term, we need to find the square root of 22 and then multiply it by the square root of 3. The square root of 22 is approximately 4.69, and the square root of 3 is approximately 1.73. Therefore, 22−−√3 simplifies to 4.69 * 1.73, which is approximately 8.10.
2. 322−−√:
To simplify this term, we need to find the square root of 32. The square root of 32 is approximately 5.66.
3. 22−−√:
To simplify this term, we need to find the square root of 22. The square root of 22 is approximately 4.69.
Now, let's add the simplified terms together:
4. 22−−√3 + 322−−√ + 22−−√:
Adding the simplified terms, we have 8.10 + 5.66 + 4.69. Calculating this sum, we get approximately 18.45.
Therefore, the result of the expression 22−−√3 + 322−−√ + 22−−√ is approximately 18.45.