Rationalize the Denominator and Simplify $\frac { \sqrt { 5 } } { \sqrt { 3 } + 7 }$

question 232

Multiple Choice

Rationalize the denominator and simplify.
- $\frac { \sqrt { 5 } } { \sqrt { 3 } + 7 }$

• A) \(\frac { \sqrt { 15 } - 7 \sqrt { 5 } } { - 46 }\)
• B) \(\frac { \sqrt { 15 } - 7 \sqrt { 5 } } { 10 }\)
• C) \(\frac { 3 \sqrt { 15 } + 3 \sqrt { 5 } } { 21 }\)
• D) \(\frac { \sqrt { 15 } + 7 \sqrt { 5 } } { - 46 }\)

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Definitions:

Wavenumber

A measure of the number of wave cycles per unit distance, often used in physics and chemistry to describe the wavelengths of light and other forms of electromagnetic radiation.

Wavelength

The distance between successive crests of a wave, especially points in a sound wave or electromagnetic wave.

Electromagnetic Radiation

Energy that travels through space in the form of waves, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

Vibrational Motions

The movement of atoms within a molecule that involves the stretching and bending of chemical bonds.