Simplify the Expression $( 10 \sqrt { 5 } + 3 \sqrt { 2 } ) ( 3 \sqrt { 5 } + 9 \sqrt { 2 } )$

question 335

Multiple Choice

Simplify the expression. Assume all variables represent positive real numbers.
- $( 10 \sqrt { 5 } + 3 \sqrt { 2 } ) ( 3 \sqrt { 5 } + 9 \sqrt { 2 } )$

• A) \(30 \sqrt { 5 } + 27 \sqrt { 2 } + 99 \sqrt { 10 }\)
• B) \(30 \sqrt { 5 } + 27 \sqrt { 2 }\)
• C) \(204 + 99 \sqrt { 10 }\)
• D) \(96 + 99 \sqrt { 10 }\)

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Definitions:

Test Statistic Value

A value derived from sample data during a hypothesis test, used to determine whether to reject the null hypothesis within the context of the test.

Significance Level

The threshold under which the p-value falls to reject the null hypothesis, typically set at 0.05 or 5%.

Critical Value

A threshold in a statistical test that defines the boundary between where a statistical hypothesis would be considered significantly different or not.

Null Hypothesis

A default hypothesis that there is no significant difference or effect, to be tested against the alternative hypothesis.