Pertanyaan

5 + 2 6 4 = ....

$\frac{4}{5 + 2 6} = ....$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah

nilai dari $fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction$ adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 square root of 3 minus 4 square root of 2. end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 square root of 3 minus 4 square root of 2. end cell end table

Pembahasan

Berdasarkan sifat bilangan akar yaitu maka Ketika ada penyebut berbentuk akar maka perlu dilakukan rasionalisasi bentuk akar dengan mengalikan akar sekawanannya sehingga diperoleh Jadi nilai dari adalah

Berdasarkan sifat bilangan akar yaitu square root of open parentheses a plus b close parentheses plus-or-minus 2 square root of a. b end root end root equals square root of a plus-or-minus square root of b maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction end cell equals cell fraction numerator 4 over denominator square root of open parentheses 2 plus 3 close parentheses plus 2 square root of 2 cross times 3 end root end root end fraction end cell row cell fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction end cell equals cell fraction numerator 4 over denominator square root of 2 plus square root of 3 end fraction end cell end table$

Ketika ada penyebut berbentuk akar maka perlu dilakukan rasionalisasi bentuk akar dengan mengalikan akar sekawanannya sehingga diperoleh

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction end cell equals cell fraction numerator 4 over denominator square root of 2 plus square root of 3 end fraction end cell row cell fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction end cell equals cell fraction numerator 4 over denominator square root of 2 plus square root of 3 end fraction cross times fraction numerator square root of 2 minus square root of 3 over denominator square root of 2 minus square root of 3 end fraction end cell row cell fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction end cell equals cell fraction numerator 4 open parentheses square root of 2 minus square root of 3 close parentheses over denominator open parentheses square root of 2 cross times square root of 2 close parentheses up diagonal strike negative open parentheses square root of 2 cross times square root of 3 close parentheses plus open parentheses square root of 2 cross times square root of 3 close parentheses end strike minus open parentheses square root of 3 cross times square root of 3 close parentheses end fraction end cell row cell fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction end cell equals cell fraction numerator 4 open parentheses square root of 2 minus square root of 3 close parentheses over denominator 2 minus 3 end fraction end cell row cell fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction end cell equals cell fraction numerator 4 open parentheses square root of 2 minus square root of 3 close parentheses over denominator negative 1 end fraction end cell row cell fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction end cell equals cell 4 square root of 3 minus 4 square root of 2 end cell end table end style$

Jadi nilai dari $fraction numerator 4 over denominator square root of 5 plus 2 square root of 6 end root end fraction$ adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 square root of 3 minus 4 square root of 2. end cell end table