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

Math
154856
Cancel the common factor of 15 and 48.
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Factor 3 out of 15.
3(5)4856
Cancel the common factors.
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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.
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Rewrite 56 as 56.
51656
Multiply 56 by 66.
516(56⋅66)
Combine and simplify the denominator.
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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
Add 1 and 1.
5165662
Rewrite 62 as 6.
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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.
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Cancel the common factor.
51656622
Divide 1 by 1.
5165661
5165661
Evaluate the exponent.
516566
516566
516566
Simplify the numerator.
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Combine using the product rule for radicals.
5165⋅66
Multiply 5 by 6.
516306
516306
516306
Simplify terms.
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Combine 16 and 306.
516306
Reduce the expression 16306 by cancelling the common factors.
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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.
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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
Add 1 and 1.
53308302
Rewrite 302 as 30.
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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.
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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.
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Factor 3 out of 330.
53(30)8⋅30
Cancel the common factors.
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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.
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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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