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