Simplify (3 square root of 8a^2- square root of 2a)/( square root of 2a)

Math
38a2-2a2a
Simplify the numerator.
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Rewrite 8a2 as (2a)2⋅2.
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Factor 4 out of 8.
34(2)a2-2a2a
Rewrite 4 as 22.
322⋅2a2-2a2a
Move 2.
322a2⋅2-2a2a
Rewrite 22a2 as (2a)2.
3(2a)2⋅2-2a2a
3(2a)2⋅2-2a2a
Pull terms out from under the radical.
3(2a2)-2a2a
Multiply 2 by 3.
6a2-2a2a
6a2-2a2a
Multiply 6a2-2a2a by 2a2a.
6a2-2a2a⋅2a2a
Combine and simplify the denominator.
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Multiply 6a2-2a2a and 2a2a.
(6a2-2a)2a2a2a
Raise 2a to the power of 1.
(6a2-2a)2a2a12a
Raise 2a to the power of 1.
(6a2-2a)2a2a12a1
Use the power rule aman=am+n to combine exponents.
(6a2-2a)2a2a1+1
Add 1 and 1.
(6a2-2a)2a2a2
Rewrite 2a2 as 2a.
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Use axn=axn to rewrite 2a as (2a)12.
(6a2-2a)2a((2a)12)2
Apply the power rule and multiply exponents, (am)n=amn.
(6a2-2a)2a(2a)12⋅2
Combine 12 and 2.
(6a2-2a)2a(2a)22
Cancel the common factor of 2.
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Cancel the common factor.
(6a2-2a)2a(2a)22
Divide 1 by 1.
(6a2-2a)2a(2a)1
(6a2-2a)2a(2a)1
Simplify.
(6a2-2a)2a2a
(6a2-2a)2a2a
(6a2-2a)2a2a
Apply the distributive property.
6a22a-2a2a2a
Multiply 6a22a.
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Combine using the product rule for radicals.
6a2a⋅2-2a2a2a
Multiply 2 by 2.
6a4a-2a2a2a
6a4a-2a2a2a
Multiply -2a2a.
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Raise 2a to the power of 1.
6a4a-(2a12a)2a
Raise 2a to the power of 1.
6a4a-(2a12a1)2a
Use the power rule aman=am+n to combine exponents.
6a4a-2a1+12a
Add 1 and 1.
6a4a-2a22a
6a4a-2a22a
Simplify each term.
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Rewrite 4 as 22.
6a22a-2a22a
Pull terms out from under the radical.
6a(2a)-2a22a
Multiply 2 by 6.
12aa-2a22a
Rewrite 2a2 as 2a.
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Use axn=axn to rewrite 2a as (2a)12.
12aa-((2a)12)22a
Apply the power rule and multiply exponents, (am)n=amn.
12aa-(2a)12⋅22a
Combine 12 and 2.
12aa-(2a)222a
Cancel the common factor of 2.
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Cancel the common factor.
12aa-(2a)222a
Divide 1 by 1.
12aa-(2a)12a
12aa-(2a)12a
Simplify.
12aa-(2a)2a
12aa-(2a)2a
Multiply 2 by -1.
12aa-2a2a
12aa-2a2a
Simplify terms.
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Factor 2a out of 12aa-2a.
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Factor 2a out of 12aa.
2a(6a)-2a2a
Factor 2a out of -2a.
2a(6a)+2a(-1)2a
Factor 2a out of 2a(6a)+2a(-1).
2a(6a-1)2a
2a(6a-1)2a
Cancel the common factor of 2.
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Cancel the common factor.
2a(6a-1)2a
Rewrite the expression.
a(6a-1)a
a(6a-1)a
Cancel the common factor of a.
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Cancel the common factor.
a(6a-1)a
Divide 6a-1 by 1.
6a-1
6a-1
6a-1
Simplify (3 square root of 8a^2- square root of 2a)/( square root of 2a)

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