square root of 17find the square root of 17
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Answered by
3
Answer:
√17
is not simplifiable and is irrational.
We can calculate rational approximations like:
√17
≈26865≈4.1231
Explanation:
Since
17
is prime, it has no square factors, so
√17
cannot be simplified.
It is an irrational number a little larger than
4
.
Since
17=
42
+1
is in the form
n2
+1
,
√17
has a particularly simple continued fraction expansion:
√17
=
[4;
¯8
]
=4+1
8+
1
8+1
8+1
8+1
8+1
8+...
You can terminate this continued fraction expansion early to get rational approximations to
√17
.
For example:
√17
≈
[4;8,8]
=4+1
8+
18
=4+865
=
26865
=4.1
¯¯¯¯¯¯¯¯¯¯¯¯230769
Actually:
√17
≈4.12310562561766054982
20
√17
is not simplifiable and is irrational.
We can calculate rational approximations like:
√17
≈26865≈4.1231
Explanation:
Since
17
is prime, it has no square factors, so
√17
cannot be simplified.
It is an irrational number a little larger than
4
.
Since
17=
42
+1
is in the form
n2
+1
,
√17
has a particularly simple continued fraction expansion:
√17
=
[4;
¯8
]
=4+1
8+
1
8+1
8+1
8+1
8+1
8+...
You can terminate this continued fraction expansion early to get rational approximations to
√17
.
For example:
√17
≈
[4;8,8]
=4+1
8+
18
=4+865
=
26865
=4.1
¯¯¯¯¯¯¯¯¯¯¯¯230769
Actually:
√17
≈4.12310562561766054982
20
Gunjan2003:
good explination
Answered by
0
square root of 17 is 4.12.......
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