Without using a calculator, determine between which two consecutive integers the square root lies.
√83
< √83 <
(Simplify your answer.)
We can estimate the square root of 83 by finding the perfect squares on either side of it.
The perfect square smaller than 83 is 81 (which is equal to 9^2) and the perfect square greater than 83 is 100 (which is equal to 10^2).
So, we can conclude that √83 is between 9 and 10.
Therefore, 9 < √83 < 10.
To determine between which two consecutive integers the square root of 83 lies, we can use some estimation and basic arithmetic.
First, let's find the perfect squares that are close to 83. The perfect squares before and after 83 are 81 (9^2) and 100 (10^2), respectively. Since the square root is between 9 and 10, we can conclude that the square root of 83 is between these two numbers.
Therefore, √83 can be estimated as between 9 and 10.
To determine between which two consecutive integers the square root of 83 lies, we can estimate the value of √83.
First, let's find consecutive perfect squares that √83 falls between:
√81 = 9
√100 = 10
Since 81 is smaller than 83, and 100 is larger than 83, we can conclude that √83 lies between the integers 9 and 10.