Question

Simplify the expression. $$ \sqrt{3}(5 \sqrt{2}+\sqrt{3}) $$

   Simplify the expression.
$$
\sqrt{3}(5 \sqrt{2}+\sqrt{3})
$$

Algebra 1: Concepts and Skills

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 12, Problem 33

Instant Answer

Solved by Expert Heather Zimmers

04/18/2020

Step 1

This gives us $\sqrt{3} \cdot 5\sqrt{2} + \sqrt{3} \cdot \sqrt{3}$. Show more…

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Simplify the expression. $$ \sqrt{3}(5 \sqrt{2}+\sqrt{3}) $$

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Key Concepts

Distributive Property

The distributive property allows one to multiply a term by each addend inside parentheses separately. In algebra, this property is crucial for simplifying expressions by eliminating parentheses, as it applies the operation uniformly across all terms within the expression.

Multiplication of Radicals

When multiplying square roots, the property ?a * ?b = ?(ab) is used. This rule helps to simplify expressions involving radicals by combining them into a single radical, provided the numbers under the radicals are nonnegative.

Combining Like Radicals

Like radicals have the same radicand and can be added or subtracted by simply combining their coefficients. This concept is similar to combining like terms in polynomial expressions and is essential in simplifying the sum of radical expressions.

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