Finite Math Examples

$1$ , $2$ , $4$ , $7$ , $9$ , $10$

The quadratic mean (rms) of a set of numbers is the square root of the sum of the squares of the numbers divided by the number of terms.

$\sqrt{\frac{{(1)}^{2} + {(2)}^{2} + {(4)}^{2} + {(7)}^{2} + {(9)}^{2} + {(10)}^{2}}{6}}$

Simplify the result.

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Remove parentheses.

$\sqrt{\frac{1^{2} + {(2)}^{2} + {(4)}^{2} + {(7)}^{2} + {(9)}^{2} + {(10)}^{2}}{6}}$

One to any power is one.

$\sqrt{\frac{1 + {(2)}^{2} + {(4)}^{2} + {(7)}^{2} + {(9)}^{2} + {(10)}^{2}}{6}}$

Remove parentheses.

$\sqrt{\frac{1 + 2^{2} + {(4)}^{2} + {(7)}^{2} + {(9)}^{2} + {(10)}^{2}}{6}}$

Raise $2$ to the power of $2$ .

$\sqrt{\frac{1 + 4 + {(4)}^{2} + {(7)}^{2} + {(9)}^{2} + {(10)}^{2}}{6}}$

Remove parentheses.

$\sqrt{\frac{1 + 4 + 4^{2} + {(7)}^{2} + {(9)}^{2} + {(10)}^{2}}{6}}$

Raise $4$ to the power of $2$ .

$\sqrt{\frac{1 + 4 + 16 + {(7)}^{2} + {(9)}^{2} + {(10)}^{2}}{6}}$

Remove parentheses.

$\sqrt{\frac{1 + 4 + 16 + 7^{2} + {(9)}^{2} + {(10)}^{2}}{6}}$

Raise $7$ to the power of $2$ .

$\sqrt{\frac{1 + 4 + 16 + 49 + {(9)}^{2} + {(10)}^{2}}{6}}$

Remove parentheses.

$\sqrt{\frac{1 + 4 + 16 + 49 + 9^{2} + {(10)}^{2}}{6}}$

Raise $9$ to the power of $2$ .

$\sqrt{\frac{1 + 4 + 16 + 49 + 81 + {(10)}^{2}}{6}}$

Remove parentheses.

$\sqrt{\frac{1 + 4 + 16 + 49 + 81 + 10^{2}}{6}}$

Raise $10$ to the power of $2$ .

$\sqrt{\frac{1 + 4 + 16 + 49 + 81 + 100}{6}}$

Add $1$ and $4$ .

$\sqrt{\frac{5 + 16 + 49 + 81 + 100}{6}}$

Add $5$ and $16$ .

$\sqrt{\frac{21 + 49 + 81 + 100}{6}}$

Add $21$ and $49$ .

$\sqrt{\frac{70 + 81 + 100}{6}}$

Add $70$ and $81$ .

$\sqrt{\frac{151 + 100}{6}}$

Add $151$ and $100$ .

$\sqrt{\frac{251}{6}}$

Divide $251$ by $6$ .

$\sqrt{41.8\overline{3}}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{41.8\overline{3}}$

Decimal Form:

$6.46786930 \dots$

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