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Exercises Expressions, exponents and radicals

Example 7.3 from Prealgebra, 7.1 Rational and Irrational Numbers

Rational and Irrational Numbers: example 7.3

Identify each of the following as 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.

Solution
ⓐ The number $36$ is a perfect square, since $6^{2} = 36 .$ So $\sqrt{36} = 6 .$ Therefore $\sqrt{36}$ is rational.
ⓑ Remember that $6^{2} = 36$ and $7^{2} = 49,$ so $44$ is not a perfect square.
This means $\sqrt{44}$ is irrational.

Your turn

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

Identify each of the following as rational or irrational:

ⓐ $\sqrt{81}$
ⓑ $\sqrt{17}$

How did it go?

PreviousRational and Irrational Numbers: example 7.2 Next Rational and Irrational Numbers: example 7.4

From Prealgebra (1st edition) by OpenStax (Rice University), section 7.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.