SASSAS
SASSAS SASSAS
  • 24-04-2017
  • Mathematics
contestada

Simplify (2sqrt5+3sqrt7)^2. Show your work. Justify each step

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LammettHash
LammettHash LammettHash
  • 24-04-2017
[tex](2\sqrt5+3\sqrt7)^2=(2\sqrt5+3\sqrt7)(2\sqrt5+3\sqrt7)[/tex]

by definition of exponentiation;

[tex]=2\sqrt5(2\sqrt5+3\sqrt7)+3\sqrt7(2\sqrt5+3\sqrt7)[/tex]
[tex]=(2\sqrt5)^2+6\sqrt{35}+6\sqrt{35}+(3\sqrt7)^2[/tex]

by the distributive property of multiplication;

[tex]=2^2(\sqrt5)^2+3^2(\sqrt7)^2+12\sqrt{35}[/tex]

by the distributive property of exponentiation;

[tex]=20+63+12\sqrt{35}[/tex]
[tex]=83+12\sqrt{35}[/tex]

by grouping common terms and simplifying.
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