# Multiply (2 square root of 3+4)(3 square root of 3-2) (23+4)(33-2)
Expand (23+4)(33-2) using the FOIL Method.
Apply the distributive property.
23(33-2)+4(33-2)
Apply the distributive property.
23(33)+23⋅-2+4(33-2)
Apply the distributive property.
23(33)+23⋅-2+4(33)+4⋅-2
23(33)+23⋅-2+4(33)+4⋅-2
Simplify and combine like terms.
Simplify each term.
Multiply 23(33).
Multiply 3 by 2.
633+23⋅-2+4(33)+4⋅-2
Raise 3 to the power of 1.
6(313)+23⋅-2+4(33)+4⋅-2
Raise 3 to the power of 1.
6(3131)+23⋅-2+4(33)+4⋅-2
Use the power rule aman=am+n to combine exponents.
631+1+23⋅-2+4(33)+4⋅-2
632+23⋅-2+4(33)+4⋅-2
632+23⋅-2+4(33)+4⋅-2
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
6(312)2+23⋅-2+4(33)+4⋅-2
Apply the power rule and multiply exponents, (am)n=amn.
6⋅312⋅2+23⋅-2+4(33)+4⋅-2
Combine 12 and 2.
6⋅322+23⋅-2+4(33)+4⋅-2
Cancel the common factor of 2.
Cancel the common factor.
6⋅322+23⋅-2+4(33)+4⋅-2
Divide 1 by 1.
6⋅31+23⋅-2+4(33)+4⋅-2
6⋅31+23⋅-2+4(33)+4⋅-2
Evaluate the exponent.
6⋅3+23⋅-2+4(33)+4⋅-2
6⋅3+23⋅-2+4(33)+4⋅-2
Multiply 6 by 3.
18+23⋅-2+4(33)+4⋅-2
Multiply -2 by 2.
18-43+4(33)+4⋅-2
Multiply 3 by 4.
18-43+123+4⋅-2
Multiply 4 by -2.
18-43+123-8
18-43+123-8
Subtract 8 from 18.
10-43+123
10+83
10+83
The result can be shown in multiple forms.
Exact Form:
10+83
Decimal Form:
23.85640646…
Multiply (2 square root of 3+4)(3 square root of 3-2)

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