Part A: Find a rational number that is between 5.2 and 5.5, Explain why it is rational. (2 points) Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the
nearest hundredth.

9514 1404 393

  A. 5.3

  B. √29 ≈ 5.39

Step-by-step explanation:

A terminating decimal is a rational number. A terminating decimal between 5.2 and 5.5 is 5.3.

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The squares of 5.2 and 5.5 are 27.04 and 30.25, respectively. Any value between these numbers that is not a perfect square will have an irrational square root. For example, √29 ≈ 5.39 is irrational.

Step-by-step explanation:

Part A

5.3

This is rational because it can be represented as 53/10

5 3/10

5 * 10 + 3 / 10

(50 + 3) / 10

53/10 which is a rational fraction.

Part B

You want something irrational between 5.2 and 5.5. You can take the square root of something like sqrt(29.16) which is 5.4 squared.

To make it irrational just add a small amount to 29.16 which would be .02 tp get  29.18

Square root 29.18 = 5.401851534

This is irrational because you cannot represent the number as a fraction. You can test the notion by asking what the next digit after 34 at the end is. You have no better that a 1 in 10 chance of getting it right. Did you guess 4? If you did, that was just luck. Here is a more complete square root, but still not rational.

5.4018515344278020984773871207007

If you are using windows on your computer, this number comes from the calculator that is included with windows. What comes after 007? I don't have a way of telling you. The result is irrational.