To determine how many numbers lie between the squares of 34 and 35, follow these steps:
1. Calculate the square of 34:
[tex]\[
34^2 = 1156
\][/tex]
2. Calculate the square of 35:
[tex]\[
35^2 = 1225
\][/tex]
3. Identify the numbers between 1156 and 1225:
The numbers lying between the squares of 34 and 35 are those numbers that are greater than 1156 and less than 1225 (excluding 1156 and 1225 themselves).
4. Count the numbers between these two squares:
To count the numbers between 1156 and 1225, we start from 1157 up to 1224.
5. Formulate the range:
The first number greater than 1156 is 1157, and the last number below 1225 is 1224. Therefore, the range of numbers we need to count is from 1157 to 1224.
6. Determine the total count:
To find out the number of integers in the range from 1157 to 1224, we can use the formula for counting integers between two given numbers, [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[
\text{Count} = b - a + 1
\][/tex]
Here, [tex]\( a = 1157 \)[/tex] and [tex]\( b = 1224 \)[/tex].
[tex]\[
\text{Count} = 1224 - 1157 + 1 = 68
\][/tex]
Hence, there are 68 integers that lie between the squares of 34 and 35.
