Question

Find a rational number and an irrational number that are between 5.2 and 5.5. Include the decimal approximation of the irrational number to the nearest hundredth.

Answer 1

Answer:

• Rational: 5.39
• Irrational: √29 ≈ 5.39

Step-by-step explanation:

Any number you can write completely that has a value between the given numbers will be a suitable rational number.

There are many ways to find irrational numbers in the given range. You can make one up, such as ...

... 5.3102003000400005000006...

a non-terminating, non-repeating decimal. (This one has a pattern that makes it easy to extend, but that doesn't make it rational.)

Or, you can use roots, logs, trig functions, exponential functions, or any of the other functions we study that have irrational values. You can add, subtract, or combine them in other ways. (tan(70°)+∛20, for example) For this, I chose √29, because that square root is between the given numbers and 29 is not a perfect square.