What 2 integers is the square root of 70 between?
The Correct Answer and Explanation is :
To determine between which two integers the square root of 70 lies, we first identify perfect squares near 70. The perfect squares we should consider are:
- (8^2 = 64)
- (9^2 = 81)
Since 70 falls between these two perfect squares (64 and 81), we can conclude that:
[
8 < \sqrt{70} < 9
]
This means that the square root of 70 is between the integers 8 and 9. To further validate this, we can find approximate values for the square root.
- Estimating the Square Root:
- We know that (\sqrt{64} = 8) and (\sqrt{81} = 9). Therefore, we can make a rough estimate of (\sqrt{70}).
- By calculating (8.5^2):
[
8.5^2 = 72.25
]
This is greater than 70, so we know (\sqrt{70} < 8.5). - Next, let’s try (8.4):
[
8.4^2 = 70.56
]
This is still greater than 70. Now let’s try (8.3):
[
8.3^2 = 68.89
]
Since (68.89 < 70), we find that:
[
8.3 < \sqrt{70} < 8.4
]
- Conclusion:
- From our findings, we see that (\sqrt{70}) is between 8.3 and 8.4, which reaffirms that it is indeed between the integers 8 and 9.
Thus, the square root of 70 lies between the integers 8 and 9.