P h y t a g o r a s 20: soal & pembahasan bentuk akar

Kamis, 10 Maret 2022

soal & pembahasan bentuk akar

Soal-soal bentuk akar

$\textrm{1.} 5\sqrt{150}-2\sqrt{54}+3\sqrt{294}-3\sqrt{486}$ $= 5\sqrt{25}\sqrt{6}-2\sqrt{9}\sqrt{6}+3\sqrt{49}\sqrt{6}-3\sqrt{81}\sqrt{6}$

$=25\sqrt{6}-6\sqrt{6}+21\sqrt{6}-27\sqrt{6}$ $=13\sqrt{6}$

$\teksrm{2. }(\sqrt{3}+\sqrt{6})(\sqrt{2}-\sqrt{3})$ $=\sqrt{6}-3+\sqrt{12}-\sqrt{18}$ $=\sqrt{6}-3+2\sqrt{3}-3\sqrt{2}$

(tidak dapat dijumlahkan dan dikurangkan karena akarnya tidak sejenis)

$\teksrm{3. }(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})$ $= 3-\sqrt{6}+\sqrt{6}-2 = 3-2=1$

$\teksrm{4. }\frac{3}{\sqrt{2}}=\frac{3}{\sqrt{2}}.\frac{\sqrt{2}}{\sqrt{2}}=\frac{3\sqrt {2}}{2}$

$\textrm{5.}\frac{8}{\sqrt{7}+\sqrt{5}}=$

$\frac{8}{\sqrt{7}+\sqrt{5}}.\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}-\sqrt{5}}=\frac {8(\sqrt{7}-\sqrt{5})}{7-5}=\frac{8(\sqrt{7}-\sqrt{5})}{2}= 4 (\sqrt{7 }-\sqrt{5})$

$\textrm{6.} \frac{3+\sqrt{2}}{\sqrt{3}-\sqrt{5}}=...$

$=\frac{3+\sqrt{2}}{\sqrt{3}-\sqrt{5}}.\frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}+\sqrt {5}}=\frac{(3+\sqrt{2})(\sqrt{3}+\sqrt{5})}{3-5}$

$=\frac{3\sqrt{3}+3\sqrt{5}+\sqrt{6}+\sqrt{10}}{-2}$

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