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SMK Teknologi dan Rekayasa

Soal 12 Pecahan Bentuk Akar


Bentuk\ sederhana\ dari\ \ \frac{4-\sqrt{2}}{3+\sqrt{2}}\ \ adalah\ ....\\\\a.\ \ 2-\sqrt{2}\ \ \ \ \ \ b.\ \ 2+2\sqrt{2}\ \ \ \ \ \ c.\ \ 3-\sqrt{2}\ \ \ \ \ \ d.\ \ 1-\sqrt{2}\ \ \ \ \ \ e.\ \ 3+2\sqrt{2}
Jawaban: a

\begin{array}{rcl}\frac{4-\sqrt{2}}{3+\sqrt{2}}&=&\frac{4-\sqrt{2}}{3+\sqrt{2}}\ \times \ \frac{3-\sqrt{2}}{3-\sqrt{2}}\\\\&=&\frac{(4-\sqrt{2})(3-\sqrt{2})}{3^{2}-(\sqrt{2})^{2}}\\\\&=&\frac{12-4\sqrt{2}-3\sqrt{2}+2}{9-2}\\\\&=&\frac{14-7\sqrt{2}}{7}\\\\&=&2-\sqrt{2}\end{array}

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2 thoughts on “Soal 12 Pecahan Bentuk Akar

  1. kok jawaban nya a,padahal kan d,karna 14-7=7, 7:7=1 ,jadi 1-akar 2

    Posted by Ridha Suci Handayani | 12 Februari 2015, 10:26 PM

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