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.
ξ
ξ
ξ
ξ
ξ
β·
(
1
)
2
+
(
2
)
2
+
(
10
)
2
+
(
6
)
2
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Step-by-step explanation:
One to any power is one.
β
1
+
(
2
)
2
+
(
10
)
2
+
(
6
)
2
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise Β
2
to the power of Β
2
.
β
1
+
4
+
(
10
)
2
+
(
6
)
2
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise Β
10
to the power of Β
2
.
β
1
+
4
+
100
+
(
6
)
2
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise Β
6
to the power of Β
2
.
β
1
+
4
+
100
+
36
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise Β
4
to the power of Β
2
.
β
1
+
4
+
100
+
36
+
16
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise Β
4
to the power of Β
2
.
β
1
+
4
+
100
+
36
+
16
+
16
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise Β
6
to the power of Β
2
.
β
1
+
4
+
100
+
36
+
16
+
16
+
36
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise Β
3
to the power of Β
2
.
β
1
+
4
+
100
+
36
+
16
+
16
+
36
+
9
+
(
1
)
2
+
(
4
)
2
10
One to any power is one.
β
1
+
4
+
100
+
36
+
16
+
16
+
36
+
9
+
1
+
(
4
)
2
10
Raise Β
4
to the power of Β
2
.
β
1
+
4
+
100
+
36
+
16
+
16
+
36
+
9
+
1
+
16
10
Add Β
1
and Β
4
.
β
5
+
100
+
36
+
16
+
16
+
36
+
9
+
1
+
16
10
Add Β
5
and Β
100
.
β
105
+
36
+
16
+
16
+
36
+
9
+
1
+
16
10
Add Β
105
and Β
36
.
β
141
+
16
+
16
+
36
+
9
+
1
+
16
10
Add Β
141
and Β
16
.
β
157
+
16
+
36
+
9
+
1
+
16
10
Add Β
157
and Β
16
.
β
173
+
36
+
9
+
1
+
16
10
Add Β
173
and Β
36
.
β
209
+
9
+
1
+
16
10
Add Β
209
and Β
9
.
β
218
+
1
+
16
10
Add Β
218
and Β
1
.
β
219
+
16
10
Add Β
219
and Β
16
.
β
235
10
Cancel the common factor of Β
235
and Β
10
.
Tap for fewer steps...
Factor Β
5
out of Β
235
.
β
5
(
47
)
10
Cancel the common factors.
Tap for fewer steps...
Factor Β
5
out of Β
10
.
β
5
β
47
5
β
2
Cancel the common factor.
β
5
β
47
5
β
2
Rewrite the expression.
β
47
2
Rewrite Β
β
47
2
as Β
β
47
β
2
.
β
47
β
2
Multiply Β
β
47
β
2
by Β
β
2
β
2
.
β
47
β
2
β
β
2
β
2
Combine and simplify the denominator.
Tap for fewer steps...
Multiply Β
β
47
β
2
and Β
β
2
β
2
.
β
47
β
2
β
2
β
2
Raise Β
β
2
to the power of Β
1
.
β
47
β
2
β
2
1
β
2
Raise Β
β
2
to the power of Β
1
.
β
47
β
2
β
2
1
β
2
1
Use the power rule Β
a
m
a
n
=
a
m
+
n
to combine exponents.
β
47
β
2
β
2
1
+
1
Add Β
1
and Β
1
.
β
47
β
2
β
2
2
Rewrite Β
β
2
2
as Β
2
.
Tap for fewer steps...
Use Β
n
β
a
x
=
a
x
n
to rewrite Β
β
2
as Β
2
1
2
.
β
47
β
2
(
2
1
2
)
2
Apply the power rule and multiply exponents, Β
(
a
m
)
n
=
a
m
n
.
β
47
β
2
2
1
2
β
2
Combine Β
1
2
and Β
2
.
β
47
β
2
2
2
2
Cancel the common factor of Β
2
.
Tap for more steps...
β
47
β
2
2
1
Evaluate the exponent.
β
47
β
2
2
Simplify the numerator.
Tap for fewer steps...
Combine using the product rule for radicals.
β
47
β
2
2
Multiply Β
47
by Β
2
.
β
94
2
The result can be shown in multiple forms.
Exact Form:
β
94
2
Decimal Form:
4.84767985
β¦
