# Simplify square root of 1/99 199
Rewrite 199 as 199.
199
Any root of 1 is 1.
199
Simplify the denominator.
Rewrite 99 as 32⋅11.
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.
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.
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.
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…
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