BENTUK AKAR
A. Menyederhanakan Bentuk Akar
Bentuk akar disederhanakan dengan memisahkan bilangan yang dapat diakar.
Contoh 01
\begin{equation*} \begin{split} & \sqrt {12} = \sqrt {4 \:.\: 3} \\\\ & \sqrt {12} = 2 \sqrt{3} \end{split} \end{equation*}
Contoh 02
\begin{equation*} \begin{split} & \sqrt {50} = \sqrt {25 \:.\: 2} \\\\ & \sqrt {50} = 5 \sqrt{2} \end{split} \end{equation*}
Contoh 03
\begin{equation*} \begin{split} & \sqrt [3] {54} = \sqrt [3] {27 \:.\: 2} \\\\ & \sqrt [3] {54} = 3 \sqrt [3] {2} \end{split} \end{equation*}
B. Merasionalkan Bentuk Akar
Merasionalkan bentuk akar adalah menghilangkan bentuk akar pada penyebut dari sebuah pecahan.
Contoh 01
\begin{equation*} \begin{split} & \frac{1}{\sqrt{5}} \quad {\color {blue} \times \frac{\sqrt{5}}{\sqrt{5}}} \\\\ & \frac{\sqrt{5}}{5} \\\\ & \frac{1}{5} \sqrt{5} \end{split} \end{equation*}
Contoh 02
\begin{equation*} \begin{split} & \frac{1}{\sqrt [3] {7}} \quad {\color {blue} \times \frac{\sqrt [3] {7^2}}{\sqrt [3] {7^2}}} \\\\ & \frac{\sqrt [3] {7^2}}{\sqrt [3] {7^3}} \\\\ & \frac{1}{7} \sqrt [3] {49} \end{split} \end{equation*}
Contoh 03
\begin{equation*} \begin{split} & \frac{1}{\sqrt [5] {2^3}} \quad {\color {blue} \times \frac{\sqrt [5] {2^2}}{\sqrt [5] {2^2}}} \\\\ & \frac{\sqrt [5] {2^2}}{\sqrt [5] {2^5}} \\\\ & \frac{1}{2} \sqrt [5] {4} \end{split} \end{equation*}
Bila penyebut berupa penjumlahan akar, maka pecahan dikalikan dengan dengan sekawannya.
| Penyebut | Sekawan | Hasil Kali |
|---|---|---|
| \(\sqrt {a} + \sqrt{b}\) | \(\sqrt {a} - \sqrt{b}\) | \(a - b\) |
| \(\sqrt {a} - \sqrt{b}\) | \(\sqrt {a} + \sqrt{b}\) | \(a - b\) |
| \(\sqrt [3] {a} + \sqrt [3] {b}\) | \(\sqrt [3] {a^2} - \sqrt [3] {ab} + \sqrt [3] {b^2}\) | \(a + b\) |
| \(\sqrt [3] {a} - \sqrt [3] {b}\) | \(\sqrt [3] {a^2} + \sqrt [3] {ab} + \sqrt [3] {b^2}\) | \(a - b\) |
Contoh 01
\begin{equation*} \begin{split} & \frac{1}{\sqrt{5} + \sqrt{2}} \quad {\color {blue} \times \frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}}} \\\\ & \frac{\sqrt{5} - \sqrt{2}}{5 - 2} \\\\ & \frac{1}{3} (\sqrt{5} - \sqrt{2}) \end{split} \end{equation*}
Contoh 02
\begin{equation*} \begin{split} & \frac{1}{\sqrt [3] {7} - \sqrt [3] {2}} \quad {\color {blue} \times \frac{\sqrt [3] {7^2} + \sqrt [3] {7 \:.\: 2} + \sqrt [3] {2^2}}{\sqrt [3] {7^2} + \sqrt [3] {7 \:.\: 2} + \sqrt [3] {2^2}}} \\\\ & \frac{\sqrt [3] {7^2} + \sqrt [3] {7 \:.\: 2} + \sqrt [3] {2^2}}{7 + 3} \\\\ & \frac {1}{10} (\sqrt [3] {49} + \sqrt [3] {21} + \sqrt [3] {4}) \end{split} \end{equation*}
| RUMUS YANG DIGUNAKAN |
|---|
| \((a + b)(a - b) = a^2 - b^2\) |
| \((a + b)(a^2 - ab + b^2) = a^3 + b^3\) |
| \((a - b)(a^2 + ab + b^2) = a^3 - b^3\) |
C. Bentuk Akar di Dalam Akar
\(\sqrt{(a + b) + 2 \sqrt{ab}} = \sqrt{a} + \sqrt{b}\)
\(\sqrt{(a + b) - 2 \sqrt{ab}} = \sqrt{a} - \sqrt{b}\)
Contoh 01
\begin{equation*} \begin{split} & \sqrt{5 + 2\sqrt{6}} \\\\ & \sqrt{(3 + 2) + 2\sqrt{3 \:.\: 2}} \\\\ & \bbox[5px, border: 2px solid magenta] {\sqrt{3} + \sqrt{2}} \end{split} \end{equation*}
Contoh 02
\begin{equation*} \begin{split} & \sqrt{4 - 2\sqrt{3}} \\\\ & \sqrt{(3 + 1) - 2\sqrt{3 \:.\: 1}} \\\\ & \sqrt{3} - \sqrt{1} \\\\ & \bbox[5px, border: 2px solid magenta] {\sqrt{3} - 1} \end{split} \end{equation*}
BENTUK EKSPONEN DAN AKAR
Konsep Dasar Latihan Soal 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19
A. Bentuk Eksponen B. Bentuk Akar C. Persamaan Eksponen Sederhana D. Persiapan Ulangan 12 3 E. Download Ringkasan Kembali ke Modul SMA