Simplify square root of 1/99

Math
199
Rewrite 199 as 199.
199
Any root of 1 is 1.
199
Simplify the denominator.
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Rewrite 99 as 32⋅11.
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Factor 9 out of 99.
19(11)
Rewrite 9 as 32.
132⋅11
132⋅11
Pull terms out from under the radical.
1311
1311
Multiply 1311 by 1111.
1311⋅1111
Combine and simplify the denominator.
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Multiply 1311 and 1111.
1131111
Move 11.
113(1111)
Raise 11 to the power of 1.
113(11111)
Raise 11 to the power of 1.
113(111111)
Use the power rule aman=am+n to combine exponents.
113111+1
Add 1 and 1.
113112
Rewrite 112 as 11.
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Use axn=axn to rewrite 11 as 1112.
113(1112)2
Apply the power rule and multiply exponents, (am)n=amn.
113⋅1112⋅2
Combine 12 and 2.
113⋅1122
Cancel the common factor of 2.
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Cancel the common factor.
113⋅1122
Divide 1 by 1.
113⋅111
113⋅111
Evaluate the exponent.
113⋅11
113⋅11
113⋅11
Multiply 3 by 11.
1133
The result can be shown in multiple forms.
Exact Form:
1133
Decimal Form:
0.10050378…
Simplify square root of 1/99

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