Question

Simplify completely. $$ \sqrt{300 q^{22} t^{16}} $$

   Simplify completely.
$$
\sqrt{300 q^{22} t^{16}}
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 3rd Edition

Chapter 10, Problem 55

Instant Answer

Solved by Expert Narayan Hari

02/14/2021

Step 1

We can use the product rule of radicals to separate this into three separate square roots: $\sqrt{300} \cdot \sqrt{q^{22}} \cdot \sqrt{t^{16}}$. Show more…

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Simplify completely. $$ \sqrt{300 q^{22} t^{16}} $$

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Key Concepts

Radical Simplification

This concept involves rewriting a square root expression by separating factors inside the radical into perfect squares and remaining factors. The goal is to take the square root of the perfect squares, which simplifies the expression. It is a fundamental technique in algebra that helps reduce expressions to their simplest radical form.

Prime Factorization

Prime factorization is the process of breaking down a composite number into a product of its prime numbers. This technique is vital when simplifying radicals because it allows one to easily identify perfect square factors within the radicand, which can then be taken outside the square root.

Properties of Exponents

The properties of exponents are rules that govern how to handle powers and exponential expressions. In the context of simplifying radicals, these rules are used to manage variables with exponents, especially by recognizing that taking the square root is equivalent to raising to the one-half power. This means that if a variable is raised to an even power inside a square root, it can be expressed as the variable raised to half that exponent outside the radical.

Extraction of Perfect Squares

Extraction of perfect squares refers to identifying and removing those factors from under a square root that are themselves perfect squares. This process simplifies the radical by allowing the square root of the perfect square to be computed and expressed as a rational number or a power of a variable outside the radical.

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