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Apabila  dan , maka ....

Pertanyaan

Apabila square root of square root of square root of A end root end root equals 2 dan B equals 257, maka ....space 

  1. A greater than 8 

  2. A equals B plus 1 

  3. A equals B 

  4. B equals A plus 1 

  5. A equals B minus 1 

Pembahasan Soal:

Ingat kembali:

  • square root of a equals a to the power of 1 half end exponent 
  • a equals a to the power of 1 
  • open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent
  • table row cell a to the power of m end cell equals cell stack a cross times a cross times midline horizontal ellipsis cross times a with underbrace below end cell row blank blank cell blank presuperscript text sebanyak end text space m end presuperscript end cell end table

Dengan demikian, 

   table attributes columnalign right center left columnspacing 0px end attributes row cell square root of square root of square root of A end root end root end cell equals 2 row cell square root of square root of A to the power of 1 half end exponent end root end root end cell equals cell 2 to the power of 1 end cell row cell square root of open parentheses A to the power of 1 half end exponent close parentheses to the power of 1 half end exponent end root end cell equals cell 2 to the power of 1 end cell row cell open parentheses open parentheses A to the power of 1 half end exponent close parentheses to the power of 1 half end exponent close parentheses to the power of 1 half end exponent end cell equals cell 2 to the power of 1 end cell row cell A to the power of 1 half cross times 1 half cross times 1 half end exponent end cell equals cell 2 to the power of 1 end cell row cell A to the power of 1 over 8 end exponent end cell equals cell 2 to the power of 1 end cell row cell A to the power of 1 over 8 cross times 8 end exponent end cell equals cell 2 to the power of 1 cross times 8 end exponent end cell row cell A to the power of 1 end cell equals cell 2 to the power of 8 end cell row A equals cell 2 to the power of 8 end cell row A equals cell 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 end cell row A equals cell 4 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 end cell row A equals cell 8 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 end cell row A equals cell 16 cross times 2 cross times 2 cross times 2 cross times 2 end cell row A equals cell 32 cross times 2 cross times 2 cross times 2 end cell row A equals cell 64 cross times 2 cross times 2 end cell row A equals cell 128 cross times 2 end cell row A equals 256 end table

Oleh karena A equals 256 dan B equals 257, diperoleh hubungan

table attributes columnalign right center left columnspacing 0px end attributes row A equals 256 row blank equals cell 257 minus 1 end cell row blank equals cell B minus 1 end cell end table

dan 

table attributes columnalign right center left columnspacing 0px end attributes row B equals 257 row blank equals cell 256 plus 1 end cell row blank equals cell A plus 1 end cell end table

Jadi, apabila square root of square root of square root of A end root end root equals 2 dan B equals 257, maka B equals A plus 1 dan A equals B minus 1.

Oleh karena itu, jawaban yang benar adalah D dan E.space 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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