Finite Math Examples

$5$ , $7 i$ , $- 7 i$

Step 1

Use the formula to find the geometric mean.

$\sqrt[3]{5 \cdot (7 i) \cdot (- 7 i)}$

Step 2

Multiply $5$ by $7$ .

$\sqrt[3]{35 i \cdot - 7 i}$

Step 3

Multiply $- 7$ by $35$ .

$\sqrt[3]{- 245 i i}$

Step 4

Raise $i$ to the power of $1$ .

$\sqrt[3]{- 245 (i^{1} i)}$

Step 5

Raise $i$ to the power of $1$ .

$\sqrt[3]{- 245 (i^{1} i^{1})}$

Step 6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[3]{- 245 i^{1 + 1}}$

Step 7

Add $1$ and $1$ .

$\sqrt[3]{- 245 i^{2}}$

Step 8

Rewrite $i^{2}$ as $- 1$ .

$\sqrt[3]{- 245 \cdot - 1}$

Step 9

Multiply $- 245$ by $- 1$ .

$\sqrt[3]{245}$

Step 10

Approximate the result.

$6.25732474$

Step 11

The geometric mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$6.3$