Using rational approximations what is an equality statement comparing square 81 and square 88?
Using rational approximations, we can approximate square roots by finding the closest rational number to the given number.
For square 81, the square root is exactly 9 because 9 * 9 = 81.
For square 88, using rational approximations, we can find that the closest rational number to the square root of 88 is approximately 9.38. This means that 9.38 * 9.38 ≈ 88.
Therefore, the equality statement comparing square 81 and square 88 using rational approximations is:
9 * 9 = 81 ≈ 9.38 * 9.38.
To compare the squares of 81 and 88 using rational approximations, we can find the square root of each number and express them as decimals.
The square root of 81 is exactly 9. Its decimal approximation is 9.000.
The square root of 88 is approximately 9.38.
Since 9.38 is greater than 9.000, we can say that the square of 88 is greater than the square of 81.
Thus, the equality statement comparing the squares of 81 and 88 would be: 81^2 < 88^2.
To find a rational approximation for the squares of 81 and 88, we can start by calculating their actual values.
The square of 81 can be found by multiplying 81 by 81:
81^2 = 6561
Similarly, the square of 88 can be found by multiplying 88 by 88:
88^2 = 7744
Now, we can use rational approximations to compare the two square values.
For 6561, we can express it as a ratio using the closest rational number. One possible approximation for 6561 is 6400, which is 80^2. So, we can write:
81^2 ≈ 6400
For 7744, we can again use the closest rational number. One option is 8100, which is 90^2. So, we can write:
88^2 ≈ 8100
Therefore, the equality statement comparing the squares of 81 and 88 using rational approximations is:
81^2 ≈ 6400
88^2 ≈ 8100