Menentukan Akar Kuadrat dengan cara bersusun (Metode Ekstraksi)

Ada beberapa cara yang dapat kita lakukan untuk mencari nilai akar kuadrat dari suatu bilangan. Cara termudah pastinya dengan menggunakan kalkulator. Namun bila kita kebetulan tidak membawa alat hitung tersebut, kita dapat menentukan akar kuadrat suatu bilangan dengan cara manual yaitu dengan cara bersusun. Ingin tahu atau untuk mengingat-ingat lagi, berikut ini cara dan contohnya:

Contoh 1

Tentukan hasil dari akar-akar bilangan berikut dengan menggunakan cara bersusun:

1. $\sqrt {144} $
2. $\sqrt {256} $
3. $\sqrt 3 $
4. $\sqrt {1.000} $
5. $\sqrt {0,25} $

Jawab

1. $\sqrt {144} $
$\boxed{\begin{array}{l} \hspace{2.4cm}\textcolor{red}{1}\textcolor{blue}{2}\\ \hspace{2cm}\sqrt {144} \\ \textcolor{red}{1} \times \textcolor{red}{1} = \hspace{0.6cm} \underline 1 \hspace{0.6cm} \\ \hspace{2.4cm}044\\ \textcolor{red}{2}\textcolor{blue}{2} \times \textcolor{blue}{2} = \hspace{0.3cm}\underline {044} \\ \hspace{2.8cm}0 \end{array}}$

2. $\sqrt {256} $
$\boxed{\begin{array}{l} \hspace{2.4cm}\textcolor{red}{1}\textcolor{blue}{6}\\ \hspace{2cm}\sqrt {256} \\ \textcolor{red}{1} \times \textcolor{red}{1} = \hspace{0.6cm} \underline 1 \hspace{0.6cm} \\ \hspace{2.4cm}156\\ \textcolor{red}{2}\textcolor{blue}{6} \times \textcolor{blue}{6} = \hspace{0.3cm}\underline {156} \\ \hspace{2.8cm}0 \end{array}}$

3. $\sqrt 3 $
$\boxed{\begin{array}{l} \hspace{2.4cm} \textcolor{red}{1},\textcolor{blue}{7}\textcolor{green}{3}\textcolor{yellow}2... \\ \hspace{2cm}\sqrt 3 \\ \textcolor{red}{1} \times \textcolor{red}{1} = \hspace{0.6cm} \underline 1 \\ \hspace{2.4cm}200\\ \textcolor{red}{2}\textcolor{blue}{7} \times \textcolor{blue}{7} = \hspace{0.3cm} \underline {189} \\ \hspace{2.8cm}1.100\\ \textcolor{blue}{34}\textcolor{green}{3} \times \textcolor{green}{3} = \hspace{0.4cm} \underline {1.029} \\ \hspace{3.4cm}7.100\\ \textcolor{green}{346}\textcolor{yellow}{2} \times \textcolor{yellow}{2} = \hspace{0.7cm} \underline {6.924} \end{array}}$

4. $\sqrt {1.000} $
$\boxed{\begin{array}{l} \hspace{2.4cm} \textcolor{red}{3}\textcolor{blue}{1},\textcolor{green}{6}\textcolor{yellow}{2}... \\ \hspace{2cm}\sqrt 1.000 \\ \textcolor{red}{3} \times \textcolor{red}{3} = \hspace{0.6cm} \underline 9 \\ \hspace{2.4cm}100\\ \textcolor{red}{6}\textcolor{blue}{1} \times \textcolor{blue}{1} = \hspace{0.5cm} \underline {61} \\ \hspace{2.7cm}3.900\\ \textcolor{blue}{62}\textcolor{green}{6} \times \textcolor{green}{6} = \hspace{0.3cm} \underline {3.756} \\ \hspace{3.4cm}14.400\\ \textcolor{green}{6.32}\textcolor{yellow}{2} \times \textcolor{yellow}{2} = \hspace{0.7cm} \underline {12.644} \end{array}}$

5. $\sqrt {0,25} $
$\boxed{\begin{array}{l} \hspace{2.4cm} \textcolor{red}{0},\textcolor{blue}{5} \\ \hspace{2cm}\sqrt {0,25} \\ \textcolor{red}{0} \times \textcolor{red}{0} = \hspace{0.6cm} \underline 0 \\ \hspace{2.5cm}025\\ \textcolor{red}{0}\textcolor{blue}{5} \times \textcolor{blue}{5} = \hspace{0.6cm} \underline {25} \\ \hspace{2.8cm}0 \end{array}}$

Demikian beberapa contoh bagaimana cara untuk mencari akar dari suatu bilangan tanpa alat hitung atau kalkulator. Terima kasih