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Home › Bentuk Akar › Matematika SMP

Cara Mudah Merasionalkan Bentuk Akar

Ingat !!!

1. Merasionalkan Bentuk $\frac{a}{\sqrt{b}}$

Bentuk Umum:

Contoh 1.1

Rasionalkan Penyebut pecahan $\frac{3}{2\sqrt{5}}$

Jawab :

$\frac{3}{2\sqrt{5}}=\frac{3}{2\sqrt{5}}.\frac{2\sqrt{5}}{2\sqrt{5}}=\frac{6\sqrt{5}}{4.5}=\frac{3\sqrt{5}}{10}$
atau
$\frac{3}{2\sqrt{5}}=\frac{3}{2\sqrt{5}}.\frac{\sqrt{5}}{\sqrt{5}}=\frac{3\sqrt{5}}{2.5}=\frac{3\sqrt{5}}{10}$

2. Merasionalkan bentuk $\frac{a}{b+\sqrt{c}}$ dan $\frac{a}{b-\sqrt{c}}$
Bentuk Umum:

$\frac{a}{b+\sqrt{c}}=\frac{a}{b+\sqrt{c}}.\frac{b-\sqrt{c}}{b-\sqrt{c}}$

$\frac{a}{b-\sqrt{c}}=\frac{a}{b-\sqrt{c}}.\frac{b+\sqrt{c}}{b+\sqrt{c}}$

Contoh 1.2

Rasionalkan penyebut pecahan $\frac{6}{3+\sqrt{5}}$

Jawab :

3. Merasionalkan bentuk $\frac{a}{\sqrt{b}+\sqrt{c}}$ dan $\frac{a}{\sqrt{b}-\sqrt{c}}$
Bentuk Umum:

$\frac{a}{\sqrt{b}+\sqrt{c}}=\frac{a}{\sqrt{b}+\sqrt{c}}.\frac{\sqrt{b}-\sqrt{c}}{\sqrt{b}-\sqrt{c}}$

$\frac{a}{\sqrt{b}-\sqrt{c}}=\frac{a}{\sqrt{b}-\sqrt{c}}.\frac{\sqrt{b}+\sqrt{c}}{\sqrt{b}+\sqrt{c}}$

Contoh 1.3
Rasionalkan penyebut pecahan $\frac{8}{\sqrt{7}-\sqrt{3}}$

Jawab :