Question

which of the following choices is the geometric mean of 11 and 4?
2√11
√11
4√11

Explanation:

Step1: Recall the geometric mean formula

The geometric mean of two numbers \(a\) and \(b\) is given by \( \sqrt{ab} \).

Step2: Substitute \(a = 11\) and \(b = 4\) into the formula

We get \( \sqrt{11\times4} \).

Step3: Simplify the expression

\( \sqrt{44}=\sqrt{4\times11} \). Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \(a = 4\) and \(b = 11\)), we have \( \sqrt{4}\times\sqrt{11}=2\sqrt{11} \).

Answer:

\( 2\sqrt{11} \) (the first option)