# Finite Math Examples

, , , ,

Step 1

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.

Step 2

Step 2.1

Simplify the expression.

Step 2.1.1

Raise to the power of .

Step 2.1.2

Raise to the power of .

Step 2.1.3

Raise to the power of .

Step 2.1.4

Raise to the power of .

Step 2.1.5

Raise to the power of .

Step 2.1.6

Add and .

Step 2.1.7

Add and .

Step 2.1.8

Add and .

Step 2.1.9

Add and .

Step 2.2

Cancel the common factor of and .

Step 2.2.1

Rewrite as .

Step 2.2.2

Cancel the common factors.

Step 2.2.2.1

Rewrite as .

Step 2.2.2.2

Cancel the common factor.

Step 2.2.2.3

Rewrite the expression.

Step 2.3

Rewrite as .

Step 2.4

Multiply by .

Step 2.5

Combine and simplify the denominator.

Step 2.5.1

Multiply by .

Step 2.5.2

Raise to the power of .

Step 2.5.3

Raise to the power of .

Step 2.5.4

Use the power rule to combine exponents.

Step 2.5.5

Add and .

Step 2.5.6

Rewrite as .

Step 2.5.6.1

Use to rewrite as .

Step 2.5.6.2

Apply the power rule and multiply exponents, .

Step 2.5.6.3

Combine and .

Step 2.5.6.4

Cancel the common factor of .

Step 2.5.6.4.1

Cancel the common factor.

Step 2.5.6.4.2

Rewrite the expression.

Step 2.5.6.5

Evaluate the exponent.

Step 2.6

Simplify the numerator.

Step 2.6.1

Combine using the product rule for radicals.

Step 2.6.2

Multiply by .

Step 3

The result can be shown in multiple forms.

Exact Form:

Decimal Form: