Find a number with a square root between the
given numbers.
. 7 and 8
11 and 12
4 and 5
9 and 10
.1 and 2
3 and 4
For each given range, we can find a number with a square root between the two given numbers:
1. Between 7 and 8: The square root of 7 is approximately 2.65, and the square root of 8 is approximately 2.83. Therefore, a number with a square root between 7 and 8 is 7.5.
2. Between 11 and 12: The square root of 11 is approximately 3.32, and the square root of 12 is approximately 3.46. Therefore, a number with a square root between 11 and 12 is 11.5.
3. Between 4 and 5: The square root of 4 is 2, and the square root of 5 is approximately 2.24. Therefore, a number with a square root between 4 and 5 is 4.5.
4. Between 9 and 10: The square root of 9 is 3, and the square root of 10 is approximately 3.16. Therefore, a number with a square root between 9 and 10 is 9.5.
5. Between 1 and 2: The square root of 1 is 1, and the square root of 2 is approximately 1.41. Therefore, a number with a square root between 1 and 2 is 1.5.
6. Between 3 and 4: The square root of 3 is approximately 1.73, and the square root of 4 is 2. Therefore, a number with a square root between 3 and 4 is 3.5.
To find a number with a square root between the given numbers, you can follow these steps:
1. For the range between 7 and 8:
- Calculate the square root of the lower number: √7 ≈ 2.646.
- Calculate the square root of the higher number: √8 ≈ 2.828.
- A number with a square root between 7 and 8 would be 8, as its square root (√8) is between √7 and √8.
2. For the range between 11 and 12:
- Calculate the square root of the lower number: √11 ≈ 3.317.
- Calculate the square root of the higher number: √12 ≈ 3.464.
- A number with a square root between 11 and 12 would be 12, as its square root (√12) is between √11 and √12.
3. For the range between 4 and 5:
- Calculate the square root of the lower number: √4 = 2.
- Calculate the square root of the higher number: √5 ≈ 2.236.
- A number with a square root between 4 and 5 would be 5, as its square root (√5) is between √4 and √5.
4. For the range between 9 and 10:
- Calculate the square root of the lower number: √9 = 3.
- Calculate the square root of the higher number: √10 ≈ 3.162.
- A number with a square root between 9 and 10 would be 10, as its square root (√10) is between √9 and √10.
5. For the range between 1 and 2:
- Calculate the square root of the lower number: √1 = 1.
- Calculate the square root of the higher number: √2 ≈ 1.414.
- A number with a square root between 1 and 2 would be 2, as its square root (√2) is between √1 and √2.
6. For the range between 3 and 4:
- Calculate the square root of the lower number: √3 ≈ 1.732.
- Calculate the square root of the higher number: √4 = 2.
- A number with a square root between 3 and 4 would be 4, as its square root (√4) is between √3 and √4.
So, the numbers with their square roots between the given ranges are:
- Between 7 and 8: 8
- Between 11 and 12: 12
- Between 4 and 5: 5
- Between 9 and 10: 10
- Between 1 and 2: 2
- Between 3 and 4: 4
To find a number with a square root between the given numbers, we need to look for a number whose square root falls within the range.
Let's go through each pair of numbers:
1. For the numbers 7 and 8:
- Calculate the square root of 7: √7 ≈ 2.6458
- Calculate the square root of 8: √8 ≈ 2.8284
- There is no whole number whose square root falls between 7 and 8.
2. For the numbers 11 and 12:
- Calculate the square root of 11: √11 ≈ 3.3166
- Calculate the square root of 12: √12 ≈ 3.4641
- There is no whole number whose square root falls between 11 and 12.
3. For the numbers 4 and 5:
- Calculate the square root of 4: √4 = 2
- Calculate the square root of 5: √5 ≈ 2.2361
- The number 4 has a square root of 2, which falls between 4 and 5.
4. For the numbers 9 and 10:
- Calculate the square root of 9: √9 = 3
- Calculate the square root of 10: √10 ≈ 3.1623
- The number 9 has a square root of 3, which falls between 9 and 10.
5. For the numbers 1 and 2:
- Calculate the square root of 1: √1 = 1
- Calculate the square root of 2: √2 ≈ 1.4142
- The number 1 has a square root of 1, which falls between 1 and 2.
6. For the numbers 3 and 4:
- Calculate the square root of 3: √3 ≈ 1.7321
- Calculate the square root of 4: √4 = 2
- There is no whole number whose square root falls between 3 and 4.
So, the numbers with square roots between the given ranges are:
- For 4 and 5: the number 4
- For 9 and 10: the number 9
- For 1 and 2: the number 1