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

question 228

Multiple Choice

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
- $$\frac { \sqrt { 7 } + 5 } { \sqrt { 3 } }$$

• A) \(\frac { - 18 } { \sqrt { 21 } + 5 \sqrt { 3 } }\)
• B) \(\frac { - 18 } { \sqrt { 21 } - 5 \sqrt { 3 } }\)
• C) \(\frac { 35 } { 3 \sqrt { 21 } + 7 \sqrt { 3 } }\)
• D) \(\frac { 12 } { \sqrt { 21 } - 5 \sqrt { 3 } }\)

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Definitions:

P(A ∪ B)

The probability that at least one of two events, A or B, occurs, including the possibility that both events occur simultaneously.

P(A | B)

Conditional Probability of A given B, representing the probability of event A occurring given that event B is known to occur.

Independent Events

Two or more events where the occurrence or outcome of one event does not affect the occurrence or outcome of the other event(s), a fundamental concept in probability.

P(A | B)

Represents the conditional probability of event A occurring given that event B has occurred.