simplify the following surd√50 step by step
Answers
Steps to the Problem
Step 1: Write the square root of 50.
Step 2: Factor 50 under the square root symbol.
Step 3: Continue factoring until you have all prime numbers.
Step 4: Combine factors using exponents.
Step 5: Move bases outside of square root symbol, if possible.
Your ultimate solution should be 5 times the square root of 2 is the simplified version of the square root of 50, which, when simplified, should be 7.05.
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This can be written as
√
50
=
[
7
;
¯¯¯¯
14
]
where the bar over the
14
indicates the repeating part of the continued fraction.
We can terminate the continued fraction early to give us rational approximations for
√
50
.
For example:
√
50
≈
[
7
;
14
]
=
7
+
1
14
=
7.0
¯¯¯¯¯¯¯¯¯¯¯¯
714285
√
50
≈
[
7
;
14
,
14
]
=
7
+
1
14
+
1
14
=
7
+
14
197
≈
7.071066
In fact: