Question

Simplify. See Example 3. $$ \sqrt{\frac{19}{20}} \cdot \sqrt{\frac{20}{3}} $$

   Simplify. See Example 3.
$$
\sqrt{\frac{19}{20}} \cdot \sqrt{\frac{20}{3}}
$$

Beginning Algebra

Beginning Algebra

Margaret L. Lial,… 11th Edition

Chapter 8, Problem 38

Instant Answer

Solved by Expert Jeyasree R T

06/29/2020

Step 1

This is possible due to the property of square roots that says $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$. So, we have: $$ \sqrt{\frac{19}{20}} \cdot \sqrt{\frac{20}{3}} = \sqrt{\frac{19}{20} \cdot \frac{20}{3}} $$ Show more…

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Simplify. See Example 3. $$ \sqrt{\frac{19}{20}} \cdot \sqrt{\frac{20}{3}} $$

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Key Concepts

Simplifying Rational Expressions

This concept deals with the reduction of fractions by identifying and canceling common factors in the numerator and denominator. When fractions appear under a square root, simplifying them beforehand can make the overall radical expression easier to simplify. It plays a crucial role in making subsequent operations with the radicals more straightforward.

Properties of Radicals

This concept involves the rules that govern the manipulation of square roots. One key rule is that the product of two square roots is equivalent to the square root of the product of the radicands, provided that the numbers under the roots are nonnegative. This property is essential for simplifying expressions that involve the multiplication of radicals.

Simplifying Radical Expressions

This concept focuses on the process of reducing expressions containing radicals to their simplest form. It involves techniques such as combining like terms, rationalizing denominators, and canceling common factors inside the radicand. These techniques help in obtaining a more streamlined and comprehensible expression.

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