what is the square root of 17
Answers
Answer:
Here is your answer!!!!
square root of 17 = 4.123
Answer:
4.12310562562
Step-by-step explanation:
SOCRATIC
How do you find the square root of 17?
Algebra Square Roots and Irrational Numbers
1 Answer
Answer:
√
17
is not simplifiable and is irrational.
We can calculate rational approximations like:
√
17
≈
268
65
≈
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
=
4
2
+
1
is in the form
n
2
+
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
+
1
8
=
4
+
8
65
=
268
65
=
4.1
¯¯¯¯¯¯¯¯¯¯¯¯
230769
Actually:
√
17
≈
4.12310562561766054982