Nilai dari ...

Pertanyaan

Nilai dari $fraction numerator open parentheses square root of 6 minus square root of 3 close parentheses squared over denominator 3 minus 2 square root of 3 end fraction equals$ ...

Pembahasan Soal:

Dalam menyederhanakan pembagian bentuk akar , kita dapat menggunakan metode akar sekawan.

Hasil dari $fraction numerator open parentheses square root of 6 minus square root of 3 close parentheses squared over denominator 3 minus 2 square root of 3 end fraction equals$ :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses square root of 6 minus square root of 3 close parentheses squared over denominator 3 minus 2 square root of 3 end fraction end cell equals cell fraction numerator open parentheses square root of 6 minus square root of 3 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses over denominator 3 minus 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 6 minus 2 square root of 18 plus 3 over denominator 3 minus 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 9 minus 2 square root of 9 cross times 2 end root over denominator 3 minus 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 9 minus 2 times 3 square root of 2 over denominator 3 minus 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 9 minus 6 square root of 2 over denominator 3 minus 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 9 minus 6 square root of 2 over denominator 3 minus 2 square root of 3 end fraction cross times fraction numerator 3 plus 2 square root of 3 over denominator 3 plus 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 27 plus 18 square root of 3 minus 18 square root of 2 minus 12 square root of 6 over denominator 9 minus 4 times 3 end fraction end cell row blank equals cell fraction numerator 27 plus 18 square root of 3 minus 18 square root of 2 minus 12 square root of 6 over denominator 9 minus 12 end fraction end cell row blank equals cell fraction numerator 27 plus 18 square root of 3 minus 18 square root of 2 minus 12 square root of 6 over denominator negative 3 end fraction end cell row blank equals cell negative 9 minus 6 square root of 3 plus 6 square root of 2 plus 4 square root of 6 end cell end table$

Jadi, nilai dari $fraction numerator open parentheses square root of 6 minus square root of 3 close parentheses squared over denominator 3 minus 2 square root of 3 end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 9 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 6 end cell end table$ .

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Dwi

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 11 Juli 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Hasil dari adalah ...

Pembahasan Soal:

$table attributes columnalign right center left columnspacing 2px end attributes row cell square root of 1350 divided by square root of 3 end cell equals cell fraction numerator square root of 450 cross times 3 end root over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator square root of 450 cross times square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell square root of 450 end cell row blank equals cell square root of 25 cross times 18 end root end cell row blank equals cell square root of 25 cross times 9 cross times 2 end root end cell row blank equals cell square root of 25 cross times square root of 9 cross times square root of 2 end cell row blank equals cell 5 cross times 3 cross times square root of 2 end cell row blank equals cell 15 square root of 2 end cell end table$

Hasil dari $square root of 1350 divided by square root of 3$ adalah $15 square root of 2$

Jadi, jawaban yang tepat adalah C

Roboguru

Hasil dari adalah ...

Pembahasan Soal:

Hasil dari $fraction numerator 2 square root of 18 cross times 3 square root of 3 over denominator 3 square root of 6 end fraction$ dapat ditentukan dengan cara berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 square root of 18 cross times 3 square root of 3 over denominator 3 square root of 6 end fraction end cell equals cell fraction numerator 2 square root of 9 times 2 end root cross times 3 square root of 3 over denominator 3 square root of 6 end fraction end cell row blank equals cell fraction numerator 2 times 3 square root of 2 cross times 3 square root of 3 over denominator 3 square root of 6 end fraction end cell row blank equals cell fraction numerator 18 square root of 6 over denominator 3 square root of 6 end fraction end cell row blank equals 6 end table$

Jadi, hasil dari $fraction numerator 2 square root of 18 cross times 3 square root of 3 over denominator 3 square root of 6 end fraction$ adalah 6

Roboguru

Hasil dari adalah...

Pembahasan Soal:

Ingat operasi berikut :

$square root of a cross times square root of b equals square root of a cross times b end root square root of a divided by square root of b equals square root of a divided by b end root$

berdasarkan sifat tersebut, maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 square root of 2 cross times square root of 75 divided by square root of 54 end cell equals cell 3 square root of 2 cross times square root of 3 cross times 25 end root divided by square root of 9 cross times 6 end root end cell row blank equals cell 3 square root of 2 cross times 5 square root of 3 divided by 3 square root of 6 end cell row blank equals 5 end table$

Jadi, jawaban yang tepat adalah C.

Roboguru

Tentukan hasil pembagian akar-akar bilangan berikut! g.

Pembahasan Soal:

Ingat kembali sifat pembagian akar berikut!

Jika $a space dan space b$ sebarang bilangan bulat, maka berlaku:

$square root of a divided by square root of b equals square root of a divided by b end root$

Dengan rumus di atas, diperoleh perhitungan sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell 5 square root of 3 divided by square root of 5 end cell equals cell square root of 5 squared cross times 3 end root divided by square root of 5 end cell row blank equals cell square root of 25 cross times 3 end root divided by square root of 5 end cell row blank equals cell square root of 75 divided by square root of 5 end cell row blank equals cell square root of 75 divided by 5 end root end cell row blank equals cell square root of 15 end cell row blank blank blank end table$

Jadi, hasil dari $5 square root of 3 divided by square root of 5 equals square root of 15$ .

Roboguru

Hasil dari adalah ...

Pembahasan Soal:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 1350 divided by square root of 3 end cell equals cell square root of open parentheses 1350 divided by 3 close parentheses end root end cell row blank equals cell square root of 450 end cell row blank equals cell square root of 225 cross times 2 end root end cell row blank equals cell square root of 225 cross times square root of 2 end cell row blank equals cell 15 square root of 2 end cell end table end style$

Jadi jawaban yang tepat adalah C

Roboguru