Find the sum of the following:
56–√ − 103–√ + 36–√ +3–√
In your final answer, what is the coefficient of the term with the 3–√
?
(1 point)
Responses
-10
-10
-1
-1
8
8
-9
To solve this problem, we can simplify each term separately and then find their sum.
Starting with the first term, 56–√, we can simplify it by finding the square root of 56:
√56 = √(4 * 14) = 2√14
So, 56–√ becomes 2√14.
Moving on to the second term, -103–√, we can simplify it by finding the square root of 103:
√103 ≈ 10.15 (approximately)
Therefore, the second term remains the same: -103–√.
For the third term, 36–√, we can simplify it by finding the square root of 36:
√36 = 6
So, 36–√ becomes 6.
Finally, the last term, 3–√, is already in its simplest form.
Now, we can add up these simplified terms:
2√14 + (-103–√) + 6 + 3–√
Combining like terms, we have:
(2√14 + 6) + (-103–√ + 3–√)
Simplifying further:
2√14 + 6 -103 - √ - √ + 3
Combine the constants:
2√14 + 6 - 103 + 3
= 2√14 - 94
Therefore, the sum of the given expression is 2√14 - 94.
The coefficient of the term with the 3–√ is 1.
To find the sum of the given expression, let's simplify each term first:
56–√ = 56
103–√ = -103
36–√ = 36
3–√ = -3
Now, let's add all the simplified terms together:
56 - 103 + 36 - 3 = -10
The coefficient of the term with 3–√ is -10.
So the correct answer is -10.
To find the sum of the given terms, we need to simplify each term individually and then add them together. Let's simplify each term step by step:
1. 56 – √
The square root of a negative number is not defined, so we cannot further simplify this term. We keep it as it is.
2. 103 – √
Again, the square root of a negative number is not defined, so we cannot further simplify this term. We keep it as it is.
3. 36 – √
The square root of 36 is 6, so this term simplifies to 36 – 6 = 30.
4. 3 – √
The square root of 3 cannot be simplified further, so this term remains as 3 – √.
Now, let's add up the simplified terms:
56 – √ + 103 – √ + 36 – √ + 3 – √ = 56 + 103 + 30 + 3 – √ – √ – √ – √
Adding the numbers together, we get:
56 + 103 + 30 + 3 = 192
Now, let's count the number of √s in the expression:
There are four √ symbols present in the expression.
So, the coefficient of the term 3 – √ is 4.
Therefore, the answer is 4.