to find the estimate of square root 68 what two square root should

Question

square root of 49 and square root of 64
square root of 64 and square root of 81
square root of 67 and square root of 69
square root of 64 and square root of 69

Answer 1

To find an estimate of the square root of 68, we can use the two nearest perfect squares: 64 and 81.

1. Square root of 49 and square root of 64:
The square root of 49 is 7, and the square root of 64 is 8. So, we know that the square root of 68 will be a number between 7 and 8.

2. Square root of 64 and square root of 81:
The square root of 64 is 8, and the square root of 81 is 9. So, we know that the square root of 68 will be a number between 8 and 9.

3. Square root of 67 and square root of 69:
Since both 67 and 69 are prime numbers, we cannot find their exact square roots without using advanced mathematical techniques. Instead, we can only estimate. The square root of 67 will be slightly less than 8, while the square root of 69 will be slightly greater than 8.

4. Square root of 64 and square root of 69:
As mentioned earlier, the square root of 64 is 8, and the square root of 69 will be a number slightly greater than 8.

In summary:
- The estimate of the square root of 68 lies between the square root of 49 (7) and the square root of 64 (8).
- The estimate of the square root of 68 also lies between the square root of 64 (8) and the square root of 81 (9).
- The estimate of the square root of 68 also lies between the square root of 67 (slightly less than 8) and the square root of 69 (slightly greater than 8).
- Finally, the estimate of the square root of 68 also lies between the square root of 64 (8) and the square root of 69 (slightly greater than 8).