The Number System Unit Test
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Question
Using rational approximations, what is an inequality statement comparing 81√ and 88√? Enter <, >, or =.(1 point)
The inequality is: 81√
88√.
The inequality is 81√ < 88√.
To compare 81√ and 88√ using rational approximations, we can convert them to decimals.
Using a calculator, we find that the decimal approximation of 81√ is approximately 9. Therefore, we can rewrite 81√ as 9.
Similarly, the decimal approximation of 88√ is approximately 9.38.
Since 9 is less than 9.38, the inequality statement comparing 81√ and 88√ is:
9 < 9.38.
To compare the values 81√ and 88√ using rational approximations, we need to find the decimal approximations of these square roots.
First, let's approximate the square root of 81:
√81 = 9
Next, let's approximate the square root of 88:
√88 ≈ 9.38 (rounding to two decimal places)
Now that we have the rational approximations, we can compare them using the symbols <, >, or =.
9 < 9.38
Therefore, the inequality statement comparing 81√ and 88√ is 81√ < 88√.