Between what two integers does the square root of 75 lie?
The square root of 75 is between the integers 8 and 9.
how did you get that answer
To find the two integers between which the square root of 75 lies, we can calculate the square root of 75.
The square root of 75 is approximately 8.66025.
Rounding 8.66025 to the nearest whole number, we get 9 as the whole number greater than the square root of 75.
Therefore, the square root of 75 lies between the integers 8 and 9.
how to find the square root of 75
To find the square root of 75, you can use various methods such as long division or a calculator. Here's one method using estimation:
1. Start by finding the square root of a perfect square that is close to 75. The closest perfect square is 64, which has a square root of 8.
2. Make an estimate by comparing the value of 75 to the perfect square. Since 75 is greater than 64, we can estimate that the square root of 75 will be greater than 8.
3. Next, guess a reasonable value between 8 and 9 as the square root of 75. Let's try 8.5.
4. Square the guessed value: 8.5^2 = 72.25
5. Compare the squared guess to the original number: 72.25 is less than 75.
6. Adjust the guess accordingly. Since 72.25 is less than 75, we need to increase our guess. Let's try 8.6.
7. Square the new guess: 8.6^2 = 73.96
8. Compare the squared guess to the original number: 73.96 is less than 75.
9. Continue adjusting the guess and squaring until you find a value close enough to 75. By repeating this process, you will find that the square root of 75 is approximately 8.66025.
Please note that this method provides an estimate and the exact value of the square root of 75 is an irrational number beyond the decimal representation.
To find the range of integers between which the square root of 75 lies, we need to find the square root of 75 first.
The square root of 75 is approximately 8.6602540378.
The integer values between which the square root of 75 lies are 8 and 9.
To find the range of integers between which the square root of 75 lies, we can calculate the square root of 75 and determine the two integers that it falls between.
The square root of 75 is approximately 8.66. Now we need to find the two integers between which this value lies.
Taking the two integers closest to 8.66, we have 8 and 9. So the square root of 75 lies between the integers 8 and 9.
Note: While 8.66 is not an integer, it falls between the integers 8 and 9.