Rationalize the numerator. √((2 x)/(3 y))

Name: Problem 72, Chapter 1: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-05-06T19:11:17-08:00
Duration: 1 min 15 s
Channel: Tyler Moulton
Description: Rationalize the numerator. √((2 x)/(3 y))

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Key Concepts

Multiplying by a Form of One

Multiplying by a form of one is a strategy used to change the form of an expression without changing its value. In rationalization, one multiplies both the numerator and denominator by an expression that will eliminate the radical in the target area, ensuring the overall value of the fraction remains the same.

Properties of Exponents

The properties of exponents allow one to express radicals as expressions with fractional exponents. This conversion often facilitates the application of exponent rules such as multiplication, division, and power rules to eliminate radicals or combine like terms.

Radical Expressions

Radical expressions, including cube roots, represent roots of numbers or algebraic expressions. Working with these expressions often requires understanding how to manipulate the radicand (the expression under the root sign) and apply rules for radicals to simplify or rewrite the expression.

Rationalization

Rationalization is the process of eliminating irrational components, such as radicals, from either the numerator or the denominator of a fraction. In this context, it involves adjusting the expression so that the cube root is removed from the numerator, which can simplify further operations and comparisons.

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