ake runs 76–√ miles on Monday and 56–√ miles on Tuesday. What is the difference in miles run each day?(1 point)
Responses
212−−√
2 start root 12 end root
26–√
2 start root 6 end root
46–√
4 start root 6 end root
412−−√
The difference in miles run each day is 46–√ miles.
To find the difference in miles run each day, we need to subtract the number of miles run on Monday from the number of miles run on Tuesday.
Given that Jake runs 76–√ miles on Monday and 56–√ miles on Tuesday, the difference in miles run each day is:
56–√ - 76–√
To subtract these two values, we need to simplify the expression under the square root:
56–√ - 76–√ = 56 - 76 - 2√6
Next, we can subtract the integers:
56 - 76 = -20
So, the difference in miles run each day is -20 - 2√6, which can be written as:
-20 - 2√6
To find the difference in miles run each day, subtract the number of miles run on Tuesday from the number of miles run on Monday.
Let's start with Monday: 76 - √12 miles.
To simplify the expression with the square root, we need to determine the value of √12.
The square root of 12 is equal to √(4 × 3) = √4 × √3 = 2√3.
So, 76 - √12 becomes 76 - 2√3 miles.
Now, let's move on to Tuesday: 56 - √6 miles.
To simplify the expression with the square root, we need to determine the value of √6.
The square root of 6 is not a perfect square, so it cannot be simplified further.
So, 56 - √6 miles is the final result.
Now, to find the difference between the two days, subtract the miles run on Tuesday from the miles run on Monday: (76 - 2√3) - (56 - √6).
Performing the subtraction, we get: 76 - 2√3 - 56 + √6.
Combining like terms, the difference in miles run each day is 20 - 2√3 + √6.
So, the correct answer is: 20 - 2√3 + √6 miles.