Operasi Hitung Bentuk Akar

Menyederhanakan perhitungan bentuk akar.

a\sqrt{m}\pm b\sqrt{m} = (a\pm b)\sqrt{m}

\sqrt{a\times b}\hspace2.6em = \sqrt{a}\times \sqrt{b}

\sqrt{\dfrac{a}{b}}\hspace3.8em = \dfrac{\sqrt{a}}{\sqrt{b}}

Contoh 1:

3\sqrt{6}+5\sqrt{6}=(3+5)\sqrt{6}

\hspace4.9em =8\sqrt{6}

Contoh 2:

7\sqrt{3}-\sqrt{3}=(7-1)\sqrt{3}

\hspace4.4em =6\sqrt{3}

Contoh 3:

\sqrt{20}+\sqrt{45}=\sqrt{4\times 5}+\sqrt{9\times 5}

\hspace4.9em =\sqrt{4}\times \sqrt{5}+\sqrt{9}\times \sqrt{5}

\hspace4.9em =2\sqrt{5}+3\sqrt{5}

\hspace4.9em =(2+3)\sqrt{5}

\hspace4.9em =5\sqrt{5}

Contoh 4:

7\sqrt{6}\times 5\sqrt{2}=7\sqrt{6}\times 5\sqrt{2}

\hspace4.9em =7\times 5\times \sqrt{6}\times \sqrt{2}

\hspace4.9em =35\times \sqrt{3\times 2}\times \sqrt{2}

\hspace4.9em =35\times \sqrt{3}\times\sqrt{2}\times \sqrt{2}

\hspace4.9em =35\times \sqrt{3}\times 2

\hspace4.9em =70\sqrt{3}

Contoh 5:

\large\frac{\sqrt{28}+\sqrt{63}+\sqrt{112}}{\sqrt{7}+\sqrt{175}}=\frac{\sqrt{4.7}+\sqrt{9.7}+\sqrt{16.7}}{\sqrt{7}+\sqrt{25.7}}

\hspace6em \large=\frac{\sqrt{4.7}+\sqrt{9.7}+\sqrt{16.7}}{\sqrt{7}+\sqrt{25.7}}

\hspace6em \large=\frac{2\sqrt{7}+3\sqrt{7}+4\sqrt{7}}{\sqrt{7}+5\sqrt{7}}

\hspace6em \large=\frac{(2+3+4)\sqrt{7}}{(1+5)\sqrt{7}}

\hspace6em \large=\frac{9\sqrt{7}}{6\sqrt{7}}=\frac{9\cancel{\sqrt{7}}}{6\cancel{\sqrt{7}}}

\hspace6em \large=\frac{9}{6}=\frac{3}{2}