# Simplify square root of 16/6

166
Cancel the common factor of 16 and 6.
Factor 2 out of 16.
2(8)6
Cancel the common factors.
Factor 2 out of 6.
2⋅82⋅3
Cancel the common factor.
2⋅82⋅3
Rewrite the expression.
83
83
83
Rewrite 83 as 83.
83
Simplify the numerator.
Rewrite 8 as 22⋅2.
Factor 4 out of 8.
4(2)3
Rewrite 4 as 22.
22⋅23
22⋅23
Pull terms out from under the radical.
223
223
Multiply 223 by 33.
223⋅33
Combine and simplify the denominator.
Multiply 223 and 33.
22333
Raise 3 to the power of 1.
223313
Raise 3 to the power of 1.
2233131
Use the power rule aman=am+n to combine exponents.
22331+1
22332
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
223(312)2
Apply the power rule and multiply exponents, (am)n=amn.
223312⋅2
Combine 12 and 2.
223322
Cancel the common factor of 2.
Cancel the common factor.
223322
Divide 1 by 1.
22331
22331
Evaluate the exponent.
2233
2233
2233
Simplify the numerator.
Combine using the product rule for radicals.
23⋅23
Multiply 3 by 2.
263
263
The result can be shown in multiple forms.
Exact Form:
263
Decimal Form:
1.63299316…
Simplify square root of 16/6