Simplify 1/3* square root of 72+1/4* square root of 32-1/2* square root of 72+7/12* square root of 18

Math
13⋅72+14⋅32-12⋅72+712⋅18
Simplify each term.
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Rewrite 72 as 62⋅2.
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Factor 36 out of 72.
13⋅36(2)+14⋅32-12⋅72+712⋅18
Rewrite 36 as 62.
13⋅62⋅2+14⋅32-12⋅72+712⋅18
13⋅62⋅2+14⋅32-12⋅72+712⋅18
Pull terms out from under the radical.
13⋅(62)+14⋅32-12⋅72+712⋅18
Cancel the common factor of 3.
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Factor 3 out of 62.
13⋅(3(22))+14⋅32-12⋅72+712⋅18
Cancel the common factor.
13⋅(3(22))+14⋅32-12⋅72+712⋅18
Rewrite the expression.
22+14⋅32-12⋅72+712⋅18
22+14⋅32-12⋅72+712⋅18
Rewrite 32 as 42⋅2.
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Factor 16 out of 32.
22+14⋅16(2)-12⋅72+712⋅18
Rewrite 16 as 42.
22+14⋅42⋅2-12⋅72+712⋅18
22+14⋅42⋅2-12⋅72+712⋅18
Pull terms out from under the radical.
22+14⋅(42)-12⋅72+712⋅18
Cancel the common factor of 4.
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Factor 4 out of 42.
22+14⋅(4(2))-12⋅72+712⋅18
Cancel the common factor.
22+14⋅(42)-12⋅72+712⋅18
Rewrite the expression.
22+2-12⋅72+712⋅18
22+2-12⋅72+712⋅18
Rewrite 72 as 62⋅2.
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Factor 36 out of 72.
22+2-12⋅36(2)+712⋅18
Rewrite 36 as 62.
22+2-12⋅62⋅2+712⋅18
22+2-12⋅62⋅2+712⋅18
Pull terms out from under the radical.
22+2-12⋅(62)+712⋅18
Cancel the common factor of 2.
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Move the leading negative in -12 into the numerator.
22+2+-12⋅(62)+712⋅18
Factor 2 out of 62.
22+2+-12⋅(2(32))+712⋅18
Cancel the common factor.
22+2+-12⋅(2(32))+712⋅18
Rewrite the expression.
22+2-1⋅(32)+712⋅18
22+2-1⋅(32)+712⋅18
Multiply 3 by -1.
22+2-3⋅2+712⋅18
Rewrite 18 as 32⋅2.
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Factor 9 out of 18.
22+2-32+712⋅9(2)
Rewrite 9 as 32.
22+2-32+712⋅32⋅2
22+2-32+712⋅32⋅2
Pull terms out from under the radical.
22+2-32+712⋅(32)
Cancel the common factor of 3.
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Factor 3 out of 12.
22+2-32+73(4)⋅(32)
Factor 3 out of 32.
22+2-32+73(4)⋅(3(2))
Cancel the common factor.
22+2-32+73⋅4⋅(32)
Rewrite the expression.
22+2-32+74⋅2
22+2-32+74⋅2
Combine 74 and 2.
22+2-32+724
22+2-32+724
Find the common denominator.
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Write 22 as a fraction with denominator 1.
221+2-32+724
Multiply 221 by 44.
221⋅44+2-32+724
Multiply 221 and 44.
22⋅44+2-32+724
Write 2 as a fraction with denominator 1.
22⋅44+21-32+724
Multiply 21 by 44.
22⋅44+21⋅44-32+724
Multiply 21 and 44.
22⋅44+2⋅44-32+724
Write -32 as a fraction with denominator 1.
22⋅44+2⋅44+-321+724
Multiply -321 by 44.
22⋅44+2⋅44+-321⋅44+724
Multiply -321 and 44.
22⋅44+2⋅44+-32⋅44+724
22⋅44+2⋅44+-32⋅44+724
Combine fractions.
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Combine fractions with similar denominators.
22⋅4+2⋅4-32⋅4+724
Simplify the expression.
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Multiply 4 by 2.
82+2⋅4-32⋅4+724
Move 4 to the left of 2.
82+42-32⋅4+724
Multiply 4 by -3.
82+42-122+724
82+42-122+724
82+42-122+724
Simplify the numerator.
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Add 82 and 42.
122-122+724
Subtract 122 from 122.
0+724
Add 0 and 72.
724
724
The result can be shown in multiple forms.
Exact Form:
724
Decimal Form:
2.47487373…
Simplify 1/3* square root of 72+1/4* square root of 32-1/2* square root of 72+7/12* square root of 18

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