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Bentuk sederhana dari adalah...

Pertanyaan

Bentuk sederhana dari fraction numerator 2 square root of 54 plus 4 square root of 6 over denominator 4 square root of 8 minus 3 square root of 2 end fraction adalah...

Pembahasan Soal:

Ingat : square root of a cross times b end root equals square root of a cross times square root of b

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 square root of 54 plus 4 square root of 6 over denominator 4 square root of 8 minus 3 square root of 2 end fraction end cell equals cell fraction numerator 2 square root of 9 cross times 6 end root plus 4 square root of 6 over denominator 4 square root of 4 cross times 2 end root minus 3 square root of 2 end fraction end cell row blank equals cell fraction numerator 2 cross times 3 square root of 6 plus 4 square root of 6 over denominator 4 cross times 2 square root of 2 minus 3 square root of 2 end fraction end cell row blank equals cell fraction numerator 10 square root of 6 over denominator 5 square root of 2 end fraction end cell row blank equals cell 2 square root of 3 end cell end table

Jadi, bentuk sederhananya adalah 2 square root of 3.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Janatu

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Bentuk rasional dari  adalah ....

Pembahasan Soal:

Perhatikan bahwa

begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 8 plus square root of 60 end root over denominator square root of 12 minus 8 square root of 2 end root end fraction end cell equals cell fraction numerator square root of 8 plus square root of 4 cross times 15 end root end root over denominator square root of 12 minus left parenthesis 2 cross times 4 right parenthesis square root of 2 end root end fraction end cell row blank equals cell fraction numerator square root of 8 plus 2 square root of 15 end root over denominator square root of 12 minus 2 square root of 16 cross times 2 end root end root end fraction end cell row blank equals cell fraction numerator square root of left parenthesis 5 plus 3 right parenthesis plus 2 square root of 5 cross times 3 end root end root over denominator square root of 12 minus 2 square root of 32 end root end fraction end cell row blank equals cell fraction numerator square root of 5 plus square root of 3 over denominator square root of left parenthesis 8 plus 4 right parenthesis minus 2 square root of 8 cross times 4 end root end root end fraction end cell row blank equals cell fraction numerator square root of 5 plus square root of 3 over denominator square root of 8 minus 2 end fraction end cell row blank equals cell fraction numerator square root of 5 plus square root of 3 over denominator square root of 8 minus 2 end fraction cross times fraction numerator square root of 8 plus 2 over denominator square root of 8 plus 2 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 5 plus square root of 3 close parentheses open parentheses square root of 8 plus 2 close parentheses over denominator open parentheses square root of 8 close parentheses squared minus 2 squared end fraction end cell row blank equals cell fraction numerator open parentheses square root of 5 cross times square root of 8 close parentheses plus open parentheses square root of 3 cross times square root of 8 close parentheses plus open parentheses square root of 5 cross times 2 close parentheses plus left parenthesis square root of 3 cross times 2 right parenthesis over denominator 4 end fraction end cell row blank equals cell fraction numerator square root of 40 plus square root of 24 plus 2 square root of 5 plus 2 square root of 3 over denominator 4 end fraction end cell row blank equals cell fraction numerator 2 square root of 10 plus 2 square root of 6 plus 2 square root of 5 plus 2 square root of 3 over denominator 4 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis square root of 10 plus square root of 6 plus square root of 5 plus square root of 3 right parenthesis over denominator 4 end fraction end cell row blank equals cell fraction numerator square root of 10 plus square root of 6 plus square root of 5 plus square root of 3 over denominator 2 end fraction end cell end table end style 

Jadi bentuk rasional dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 8 plus square root of 60 end root over denominator square root of 12 minus 8 square root of 2 end root end fraction end cell end table end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 10 plus square root of 6 plus square root of 5 plus square root of 3 over denominator 2 end fraction end cell end table end style.

Dengan demikian, jawaban yang tepat adalah A.

0

Roboguru

Hasil dari   adalah….

Pembahasan Soal:

fraction numerator square root of 13 plus 2 square root of 42 end root over denominator square root of 7 minus square root of 6 end fraction equals fraction numerator square root of open parentheses 6 plus 7 close parentheses plus 2 square root of open parentheses 6 cross times 7 close parentheses end root end root over denominator square root of 7 minus square root of 6 end fraction equals fraction numerator square root of 6 plus square root of 7 over denominator square root of 7 minus square root of 6 end fraction cross times fraction numerator square root of 7 plus square root of 6 over denominator square root of 7 plus square root of 6 end fraction equals fraction numerator open parentheses square root of 6 plus square root of 7 close parentheses open parentheses square root of 7 plus square root of 6 close parentheses over denominator open parentheses square root of 7 close parentheses squared minus open parentheses square root of 6 close parentheses squared end fraction equals fraction numerator square root of 6 open parentheses square root of 7 plus square root of 6 close parentheses plus square root of 7 open parentheses square root of 7 plus square root of 6 close parentheses over denominator 7 minus 6 end fraction equals square root of 42 plus square root of 36 plus square root of 49 plus square root of 42 equals square root of 42 plus 6 plus 7 plus square root of 42 equals 13 plus 2 square root of 42  

0

Roboguru

Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Ingat bahwa begin mathsize 14px style square root of open parentheses x plus y close parentheses minus 2 square root of x y end root end root equals square root of x minus square root of y end style dengan begin mathsize 14px style x greater than y end style.

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 12 minus 2 square root of 35 end root end cell equals cell square root of open parentheses 7 plus 5 close parentheses minus 2 square root of 7 times 5 end root end root end cell row blank equals cell square root of 7 minus square root of 5 end cell end table end style 

(karena begin mathsize 14px style 7 greater than 5 end style).   

Dengan demikian, bentuk sederhana dari begin mathsize 14px style square root of 12 minus 2 square root of 35 end root end style adalah undefined.

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Perhatikan bahwa

begin mathsize 12px style fraction numerator square root of 32 over denominator square root of 12 plus square root of 108 end root end fraction minus fraction numerator square root of 48 plus 3 over denominator 2 square root of 6 end fraction equals fraction numerator square root of 16 times 2 end root over denominator square root of 12 plus square root of 4 times 27 end root end root end fraction minus fraction numerator square root of 16 times 3 end root plus 3 over denominator 2 square root of 6 end fraction equals fraction numerator 4 square root of 2 over denominator square root of 12 plus 2 square root of 27 end root end fraction minus fraction numerator 4 square root of 3 plus 3 over denominator 2 square root of 6 end fraction equals fraction numerator 4 square root of 2 over denominator square root of open parentheses 9 plus 3 close parentheses plus 2 square root of 9 times 3 end root end root end fraction minus fraction numerator 4 square root of 3 plus 3 over denominator 2 square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction equals fraction numerator 4 square root of 2 over denominator square root of 9 plus square root of 3 end fraction minus fraction numerator square root of 6 open parentheses 4 square root of 3 plus 3 close parentheses over denominator 2 times 6 end fraction equals fraction numerator 4 square root of 2 over denominator 3 plus square root of 3 end fraction minus fraction numerator open parentheses square root of 6 cross times 4 square root of 3 close parentheses plus open parentheses square root of 6 cross times 3 close parentheses over denominator 12 end fraction equals fraction numerator 4 square root of 2 open parentheses 3 minus square root of 3 close parentheses over denominator 3 squared minus open parentheses square root of 3 close parentheses squared end fraction minus fraction numerator 4 square root of 18 plus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 4 square root of 2 open parentheses 3 minus square root of 3 close parentheses over denominator 9 minus 3 end fraction minus fraction numerator 12 square root of 2 plus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 12 square root of 2 minus 4 square root of 6 over denominator 6 end fraction minus fraction numerator 12 square root of 2 plus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 24 square root of 2 minus 8 square root of 6 over denominator 12 end fraction minus fraction numerator 12 square root of 2 plus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 24 square root of 2 minus 8 square root of 6 minus 12 square root of 2 minus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 24 square root of 2 minus 12 square root of 2 minus 8 square root of 6 minus 3 square root of 6 over denominator 12 end fraction equals fraction numerator open parentheses 24 minus 12 close parentheses square root of 2 minus open parentheses 8 plus 3 close parentheses square root of 6 over denominator 12 end fraction equals fraction numerator 12 square root of 2 minus 11 square root of 6 over denominator 12 end fraction end style 

Jadi, hasil dari undefined adalah undefined.

Dengan demikian, jawaban yang tepat adalah A.

0

Roboguru

Sederhanakanlah bentuk akar bilangan berikut!

Pembahasan Soal:

Bentuk akar square root of open parentheses a plus b close parentheses plus 2 square root of a b end root end root dapat disederhanakan dengan rumus dan prosedur berikut.

square root of open parentheses a plus b close parentheses plus 2 square root of a b end root end root equals square root of a plus square root of b

Sehingga dapat ditentukan bentuk sederhana dari bentuk akar bilangan square root of 7 plus 2 square root of 10 end root sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 7 plus 2 square root of 10 end root end cell equals cell square root of open parentheses 5 plus 2 close parentheses plus 2 square root of 5 cross times 2 end root end root end cell row blank equals cell square root of 5 plus square root of 2 end cell end table 

Dengan demikian, diperoleh square root of 7 plus 2 square root of 10 end root equals square root of 5 plus square root of 2.

1

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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