# Multiply (4 square root of 5+3)(2 square root of 5+1)

(45+3)(25+1)
Expand (45+3)(25+1) using the FOIL Method.
Apply the distributive property.
45(25+1)+3(25+1)
Apply the distributive property.
45(25)+45⋅1+3(25+1)
Apply the distributive property.
45(25)+45⋅1+3(25)+3⋅1
45(25)+45⋅1+3(25)+3⋅1
Simplify and combine like terms.
Simplify each term.
Multiply 45(25).
Multiply 2 by 4.
855+45⋅1+3(25)+3⋅1
Raise 5 to the power of 1.
8(515)+45⋅1+3(25)+3⋅1
Raise 5 to the power of 1.
8(5151)+45⋅1+3(25)+3⋅1
Use the power rule aman=am+n to combine exponents.
851+1+45⋅1+3(25)+3⋅1
852+45⋅1+3(25)+3⋅1
852+45⋅1+3(25)+3⋅1
Rewrite 52 as 5.
Use axn=axn to rewrite 5 as 512.
8(512)2+45⋅1+3(25)+3⋅1
Apply the power rule and multiply exponents, (am)n=amn.
8⋅512⋅2+45⋅1+3(25)+3⋅1
Combine 12 and 2.
8⋅522+45⋅1+3(25)+3⋅1
Cancel the common factor of 2.
Cancel the common factor.
8⋅522+45⋅1+3(25)+3⋅1
Divide 1 by 1.
8⋅51+45⋅1+3(25)+3⋅1
8⋅51+45⋅1+3(25)+3⋅1
Evaluate the exponent.
8⋅5+45⋅1+3(25)+3⋅1
8⋅5+45⋅1+3(25)+3⋅1
Multiply 8 by 5.
40+45⋅1+3(25)+3⋅1
Multiply 4 by 1.
40+45+3(25)+3⋅1
Multiply 2 by 3.
40+45+65+3⋅1
Multiply 3 by 1.
40+45+65+3
40+45+65+3
43+45+65
43+105
43+105
The result can be shown in multiple forms.
Exact Form:
43+105
Decimal Form:
65.36067977…
Multiply (4 square root of 5+3)(2 square root of 5+1)

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