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Using the Product Rule to Simplify Square Roots · Physics Playground

Exercises Expressions, exponents and radicals

Example 2 from Algebra and Trigonometry, 1.3 Radicals and Rational Exponents

Using the Product Rule to Simplify Square Roots

Simplify the radical expression.

ⓐ $\sqrt{300}$
ⓑ $\sqrt{162 a^{5} b^{4}}$

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.

1
Solution
1. ⓐ
  $\begin{matrix} \sqrt{100 \cdot 3} & Factor perfect square from radicand . \\ \sqrt{100} \cdot \sqrt{3} & Write radical expression as product of radical expressions . \\ 10 \sqrt{3} & Simplify . \end{matrix}$
2. ⓑ
  $\begin{matrix} \sqrt{81 a^{4} b^{4} \cdot 2 a} & Factor perfect square from radicand . \\ \sqrt{81 a^{4} b^{4}} \cdot \sqrt{2 a} & Write radical expression as product of radical expressions . \\ 9 a^{2} b^{2} \sqrt{2 a} & Simplify . \end{matrix}$

Your turn

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

Simplify $\sqrt{50 x^{2} y^{3} z} .$

How did it go?

PreviousEvaluating Square Roots Next Using the Product Rule to Simplify the Product of Multiple 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.