The Real Numbers: example 1.112

For each number given, identify whether it is rational or irrational: ⓐ $\sqrt{36}$ ⓑ $\sqrt{44} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

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Solution
1. ⓐ Recognize that 36 is a perfect square, since $6^{2} = 36 .$ So $\sqrt{36} = 6,$ therefore $\sqrt{36}$ is rational.
2. ⓑ Remember that $6^{2} = 36$ and $7^{2} = 49,$ so 44 is not a perfect square. Therefore, the decimal form of $\sqrt{44}$ will never repeat and never stop, so $\sqrt{44}$ is irrational.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

For each number given, identify whether it is rational or irrational: ⓐ $\sqrt{81}$ ⓑ $\sqrt{17} .$

How did it go?