Rationalize the Numerator and Simplify $\frac { \sqrt { 6 } + 7 } { \sqrt { 7 } }$

question 42

Multiple Choice

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
- $\frac { \sqrt { 6 } + 7 } { \sqrt { 7 } }$

• A) \(\frac { - 43 } { \sqrt { 42 } + 7 \sqrt { 7 } }\)
• B) \(\frac { 13 } { \sqrt { 42 } - 7 \sqrt { 7 } }\)
• C) \(\frac { 42 } { 3 \sqrt { 42 } + 6 \sqrt { 7 } }\)
• D) \(\frac { - 43 } { \sqrt { 42 } - 7 \sqrt { 7 } }\)

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Definitions:

Inductance

The property of an electrical conductor that causes it to oppose a change in the current flowing through it, stored in the magnetic field created by the current.

Henry

The SI unit of inductance, defined as the inductance in a circuit when an electromotive force of one volt is produced by a current changing at one ampere per second.

Left-hand Generator Rule

A rule used to determine the direction of induced current when a conductor moves through a magnetic field, utilizing the left hand to align thumb, forefinger, and middle finger perpendicularly.

Magnetic Field

A magnetic field is a vector field that surrounds magnets and electric currents, exerting magnetic forces on moving electric charges and magnetic materials.