Which number lies between the square root of 5 and the square root of 6 on the number line?
a) 2.33333
b) 3.14
c) 5/2
d) 2.1
To determine the number that lies between the square root of 5 and the square root of 6, we need to find the average of these two numbers.
The square root of 5 is approximately 2.236 and the square root of 6 is approximately 2.449.
Adding these two values together gives us 2.236 + 2.449 ≈ 4.685.
Dividing this sum by 2 gives us 4.685/2 ≈ 2.343.
Therefore, the number that lies between the square root of 5 and the square root of 6 on the number line is approximately 2.343.
Among the answer choices, 2.33333 is the closest to 2.343.
So, the correct answer is: a) 2.33333.
To find the number that lies between the square root of 5 and the square root of 6 on the number line, we can calculate the approximate values of these square roots.
The square root of 5 is approximately 2.236.
The square root of 6 is approximately 2.449.
Now, we can see that the number 2.33333 (option a) lies between 2.236 and 2.449.
Therefore, the correct answer is (a) 2.33333.