Learn Before
Simplifying
To simplify the expression , begin by rewriting the radicand in the denominator to show its prime factors, giving . To rationalize the denominator, multiply both the numerator and the denominator by to provide the missing factors needed to create perfect fourth powers: one additional 2 and three additional 's. The expression becomes . Simplifying the denominator yields . Finally, dividing out the common numerical factor of 2 results in the simplified expression .
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.8 Roots and Radicals - Intermediate Algebra @ OpenStax
Algebra
Related
Simplifying
Simplifying
Simplifying
In technical drafting and design, it is standard practice to simplify mathematical expressions before they are included in a final report. What is the name of the process used to transform a fraction so that it no longer contains a square root in the denominator?
In a structural engineering report, a value is written as 5 / (2 * sqrt(3)). True or False: To rationalize the denominator according to standard mathematical procedures, you must multiply both the numerator and the denominator by 2 * sqrt(3).
In a laboratory setting, a researcher calculates a concentration value that results in a fraction with a square root in the denominator. To report this value in a standard format, the researcher must rationalize the denominator. Arrange the following steps in the correct order to complete this process.
In a laboratory inventory system, chemical concentration values are often simplified to meet standard reporting requirements. Match each concentration value below with the specific square root multiplier that should be used to rationalize its denominator.
Preserving Values in Technical Simplification
In professional technical reporting, when a value is expressed as a fraction with a square root in the denominator, the process of 'rationalizing' is performed to ensure that the divisor is converted from an irrational number into a(n) ________.
Standardizing Technical Documentation
Standardizing Laboratory Reporting Ratios
In technical drafting and design, maintaining efficiency in calculations is essential. When rationalizing a denominator that contains a radical which can be simplified (such as ), what is the recommended first step to ensure the arithmetic remains as simple as possible?
A machinist is calculating a tolerance ratio given as $5 / \sqrt{2}\sqrt{2}$. Which mathematical property is the machinist applying to ensure that the original value of the measurement remains unchanged during this process?
Rationalizing Denominators with Cube Roots
Rationalizing Denominators with Fourth Roots
Simplifying
Simplifying
Simplifying
Learn After
As a data technician, you are reviewing a legacy algorithm that calculates material stress limits. The algorithm contains the expression . To standardize the formula for the system, you must rationalize the denominator. After rewriting the denominator as , which of the following represents the exact factor you must recall and multiply by both the numerator and denominator to create a perfect fourth power in the denominator?
A software developer is documenting the algorithm used by a computer-aided design (CAD) tool to simplify radical expressions. For the expression , match each procedural goal with the specific mathematical expression generated during that stage of the simplification process.
A manufacturing technician is auditing a material stress formula that contains the expression . To remove the radical from the denominator, the technician's manual states that after rewriting the denominator as , both the numerator and denominator must be multiplied by .
True or False: Multiplying by correctly provides the missing factors needed to create perfect fourth powers in the denominator.
A technical documentation specialist is updating a manual for an engineering calculation tool. To correctly simplify the radical expression , arrange the following procedural steps in the correct chronological order as outlined in the standard simplification protocol.
A logistics analyst is revising a shipping cost formula that includes the term . To ensure the formula is in its most efficient standardized form for the company's database, the analyst must rationalize the denominator and simplify the expression completely. The final simplified form of this expression is ____.