# Simplify 15/(48 square root of 5/6)

154856
Cancel the common factor of 15 and 48.
Factor 3 out of 15.
3(5)4856
Cancel the common factors.
Factor 3 out of 4856.
3(5)3(1656)
Cancel the common factor.
3⋅53(1656)
Rewrite the expression.
51656
51656
51656
Simplify the denominator.
Rewrite 56 as 56.
51656
Multiply 56 by 66.
516(56⋅66)
Combine and simplify the denominator.
Multiply 56 and 66.
5165666
Raise 6 to the power of 1.
51656616
Raise 6 to the power of 1.
516566161
Use the power rule aman=am+n to combine exponents.
5165661+1
5165662
Rewrite 62 as 6.
Use axn=axn to rewrite 6 as 612.
51656(612)2
Apply the power rule and multiply exponents, (am)n=amn.
51656612⋅2
Combine 12 and 2.
51656622
Cancel the common factor of 2.
Cancel the common factor.
51656622
Divide 1 by 1.
5165661
5165661
Evaluate the exponent.
516566
516566
516566
Simplify the numerator.
Combine using the product rule for radicals.
5165⋅66
Multiply 5 by 6.
516306
516306
516306
Simplify terms.
Combine 16 and 306.
516306
Reduce the expression 16306 by cancelling the common factors.
Factor 2 out of 1630.
52(830)6
Factor 2 out of 6.
52(830)2(3)
Cancel the common factor.
52(830)2⋅3
Rewrite the expression.
58303
58303
58303
Multiply the numerator by the reciprocal of the denominator.
53830
Multiply 3830 by 3030.
5(3830⋅3030)
Combine and simplify the denominator.
Multiply 3830 and 3030.
533083030
Move 30.
53308(3030)
Raise 30 to the power of 1.
53308(30130)
Raise 30 to the power of 1.
53308(301301)
Use the power rule aman=am+n to combine exponents.
53308301+1
53308302
Rewrite 302 as 30.
Use axn=axn to rewrite 30 as 3012.
53308(3012)2
Apply the power rule and multiply exponents, (am)n=amn.
53308⋅3012⋅2
Combine 12 and 2.
53308⋅3022
Cancel the common factor of 2.
Cancel the common factor.
53308⋅3022
Divide 1 by 1.
53308⋅301
53308⋅301
Evaluate the exponent.
53308⋅30
53308⋅30
53308⋅30
Cancel the common factor of 3 and 30.
Factor 3 out of 330.
53(30)8⋅30
Cancel the common factors.
Factor 3 out of 8⋅30.
53(30)3(8⋅10)
Cancel the common factor.
53303(8⋅10)
Rewrite the expression.
5308⋅10
5308⋅10
5308⋅10
Multiply 8 by 10.
53080
Cancel the common factor of 5.
Factor 5 out of 80.
5305(16)
Cancel the common factor.
5305⋅16
Rewrite the expression.
3016
3016
The result can be shown in multiple forms.
Exact Form:
3016
Decimal Form:
0.34232659…
Simplify 15/(48 square root of 5/6)

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