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Exercises Expressions, exponents and radicals

Example 6 from Algebra and Trigonometry, 1.3 Radicals and Rational Exponents

Adding Square Roots

Add $5 \sqrt{12} + 2 \sqrt{3} .$

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
We can rewrite $5 \sqrt{12}$ as $5 \sqrt{4 \cdot 3} .$ According the product rule, this becomes $5 \sqrt{4} \sqrt{3} .$ The square root of $\sqrt{4}$ is 2, so the expression becomes $5 (2) \sqrt{3},$ which is $10 \sqrt{3} .$ Now the terms have the same radicand so we can add.
$10 \sqrt{3} + 2 \sqrt{3} = 12 \sqrt{3}$

Your turn

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

Add $\sqrt{5} + 6 \sqrt{20} .$

How did it go?

PreviousUsing the Quotient Rule to Simplify an Expression with Two Square Roots Next Subtracting Square Roots

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.