Square root of 0.00007225 is ___________.
Answers
Answer:
=>7225×10^-8
√7225 is 85 whereas √10^-8 is 10^-4
=>85×10^-4
=>0.0085
Answer:
Explanation:
The square root of
84
is an irrational number a little larger than
9
.
A square root of a number
n
, is a number
a
such that
a
2
=
n
. Actually every positive number has two square roots, but "the" square root is usually taken to mean the positive one. The two square roots of
84
are denoted
√
84
and
−
√
84
.
Note that:
9
2
=
81
<
84
<
100
=
10
2
Hence:
9
<
√
84
<
10
Since
84
is
3
19
's of the way between
81
and
100
, we can approximate
√
84
as
3
19
≈
1
6
th of the way between
9
and
10
, about
9
1
6
=
55
6
.
In fact we find:
55
2
=
3025
=
3024
+
1
=
84
⋅
6
2
+
1
Hence
55
6
is a very efficient approximation to
√
84
Consider the quadratic whose zeros are
55
+
6
√
84
and
55
−
6
√
84
:
(
x
−
(
55
+
6
√
84
)
)
(
x
−
(
55
−
6
√
84
)
)
=
x
2
−
110
x
+
1
From this we can define a sequence recursively as follows:
⎧
⎪
⎨
⎪
⎩
a
0
=
0
a
1
=
1
a
n
+
2
=
110
a
n
+
1
−
a
n
The first few terms of this sequence are:
0
,
1
,
110
,
12099
,
1330780
The ratio between successive terms of this sequence tends rapidly towards
55
+
6
√
84
So we find:
√
84
≈
1
6
(
1330780
12099
−
55
)
=
665335
6
⋅
12099
=
665335
72594
≈
9.1651513899
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