Answer:
- rational
- irrational
- irrational
- irrational
- √7, it is irrational
Step-by-step explanation:
A rational number is one that can be expressed as the ratio of two integers. All fractions that have integer numerators and (non-zero) denominators are rational numbers. Any finite decimal number, or any repeating decimal number, is a rational number. These can always be expressed as the ratio of two integers. For example, 0.4040... = 40/99, and 0.286 = 286/1000.
To make an irrational sum, at least one of the contributors must be irrational. You want an irrational 2-number sum that has 7/8 as one of the contributors. Since 7/8 is rational, the other contributor must be irrational.
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Step 1. The number 7/8 is rational.
Step 2. The desired sum is irrational.
Step 3. The rule rational + irrational = irrational applies.
Step 4. An irrational number must be chosen.
Step 5. √7 will produce an irrational sum, because it is irrational.
