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Sederhanakan bentuk akar berikut. d.

Sederhanakan bentuk akar berikut.

d. begin mathsize 14px style 7 square root of 3 plus square root of 48 minus square root of 192 end style

  1. begin mathsize 14px style horizontal ellipsis end style 

  2. begin mathsize 14px style horizontal ellipsis end style 

Jawaban:

Dengan menggunakan sifat begin mathsize 14px style square root of a b end root equals square root of a cross times square root of b end style diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 48 end cell equals cell square root of 16 cross times 3 end root end cell row blank equals cell square root of 16 cross times square root of 3 end cell row blank equals cell 4 cross times square root of 3 end cell row blank equals cell 4 square root of 3 end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 192 end cell equals cell square root of 64 cross times 3 end root end cell row blank equals cell square root of 64 cross times square root of 3 end cell row blank equals cell 8 cross times square root of 3 end cell row blank equals cell 8 square root of 3 end cell end table end style

Selanjutnya, dengan menggunakan sifat penjumlahan dan pengurangan bentuk akar dengan bilangan pokok sama

begin mathsize 14px style a square root of c plus-or-minus b square root of c equals open parentheses a plus-or-minus b close parentheses square root of c end style

diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 7 square root of 3 plus square root of 48 minus square root of 192 end cell equals cell 7 square root of 3 plus 4 square root of 3 minus 8 square root of 3 end cell row blank equals cell open parentheses 7 plus 4 minus 8 close parentheses square root of 3 end cell row blank equals cell 3 square root of 3 end cell end table end style

Jadi, bentuk sederhana dari begin mathsize 14px style 7 square root of 3 plus square root of 48 minus square root of 192 end style adalah begin mathsize 14px style 3 square root of 3 end style.

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