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Exercises Expressions, exponents and radicals

Example 8 from Algebra and Trigonometry, 1.3 Radicals and Rational Exponents

Rationalizing a Denominator Containing a Single Term

Write $\frac{2 \sqrt{3}}{3 \sqrt{10}}$ in simplest form.

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 radical in the denominator is $\sqrt{10} .$ So multiply the fraction by $\frac{\sqrt{10}}{\sqrt{10}} .$ Then simplify.

$\begin{array}{l} \frac{2 \sqrt{3}}{3 \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}} \\ \frac{2 \sqrt{30}}{30} \\ \frac{\sqrt{30}}{15} \end{array}$

Your turn

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

Write $\frac{12 \sqrt{3}}{\sqrt{2}}$ in simplest form.

How did it go?

PreviousSubtracting Square Roots Next Rationalizing a Denominator Containing Two Terms

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 1.3, 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.