$\"\"$

Geometric mean is positive number x of two positive numbers where the proportion

a : x = x : b is true.

The proportion can be written as fraction $\"\"$ .

Find geometric mean of 36 and 49.

Write the proportion from the definition of geometric mean.

$\"\"$

$\"\"$ (Apply cross products property)

$\"\"$ (Multiply: $\"\"$ $\"\"$ )

$\"\"$ (Take the positive square root of each side)

$\"\"$ ( $\"\"$ ) $\"\"$

The geometric mean of 36 and 49 is 42.