1)i	\begin{align*} &\sqrt{3669}\\ \end{align*} \begin{align*} &\text{ }\text{ }\text{ }\text{ }60.572\\ 6 &\big|\overline{3669}\\ &\big|\underline{36}\\ 120&\big|\text{ }\text{ }069\\ &\big|\underline{\text{ }\text{ }0}\\ 1205&\big|\text{ }\text{ }\text{ }\text{ }6900\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }6025}\\ 12107&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }87500\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }84749}\\ 121142&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }275100\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }242284}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }32816\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{60.57}} \end{align*}	ii	\begin{align*} &\sqrt{4302}\\ \end{align*} \begin{align*} &\text{ }\text{ }\text{ }\text{ }65.589\\ 6 &\big|\overline{4302}\\ &\big|\underline{36}\\ 125&\big|\text{ }\text{ }702\\ &\big|\underline{\text{ }\text{ }625}\\ 1305&\big|\text{ }\text{ }\text{ }\text{ }7700\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }6525}\\ 13108&\big|\text{ }\text{ }\text{ }\text{ }117500\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }104864}\\ 131169&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }12636\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{65.59}} \end{align*}	iii	\begin{align*} &\sqrt{22.79}\\ \end{align*} \begin{align*} &\text{ }\text{ }\text{ }\text{ }4.773\\ 4 &\big|\overline{22.79}\\ &\big|\underline{16}\\ 87&\big|\text{ }\text{ }679\\ &\big|\underline{\text{ }\text{ }609}\\ 947&\big|\text{ }\text{ }\text{ }\text{ }7000\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }6629}\\ 9543&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }37100\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }28629}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }8471\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{4.77}} \end{align*}
iv	\begin{align*} &\sqrt{0.1296}\\ \end{align*} \begin{align*} &\text{ }\text{ }\text{ }\text{ }0.360\\ 0 &\big|\overline{0.1296}\\ &\big|\underline{0}\\ 3&\big|012\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }9}\\ 66&\big|\text{ }\text{ }\text{ }\text{ }396\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }396}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }0\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{0.36}} \end{align*}	v	\begin{align*} &\sqrt{5.344}\\ \end{align*} \begin{align*} &\text{ }\text{ }\text{ }\text{ }2.311\\ 2 &\big|\overline{5.344}\\ &\big|\underline{4}\\ 43&\big|134\\ &\big|\underline{129}\\ 461&\big|\text{ }\text{ }\text{ }\text{ }540\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }461}\\ 4621&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }7900\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }4621}\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{2.31}} \end{align*}
2)	\begin{align*} &l^2=25^2+12^2\\[5pt] &l^2=625+144\\[5pt] &l^2=\sqrt{769}\\[5pt] &=\underline{\underline{28m}} \end{align*}	\begin{align*} &\text{ }\text{ }\text{ }\text{ }27.7\\ 2 &\big|\overline{769}\\ &\big|\underline{4}\\ 47&\big|369\\ &\big|\underline{329}\\ 547&\big|\text{ }\text{ }4000\\ &\big|\underline{\text{ }\text{ }3829}\\ &\big|\text{ }\text{ }\text{ }\text{ }171\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{28m}} \end{align*}
3)	\begin{align*} &x^2+x^2=12^2\\[5pt] &2x^2=144\\[5pt] &x=72\\[5pt] &x=\sqrt{72}\\[5pt] &=\underline{\underline{8.49m}} \end{align*}	\begin{align*} &\text{ }\text{ }\text{ }\text{ }8.485\\ 8 &\big|\overline{72}\\ &\big|\underline{64}\\ 164&\big|\text{ }\text{ }800\\ &\big|\underline{\text{ }\text{ }656}\\ 1688&\big|\text{ }\text{ }14400\\ &\big|\underline{\text{ }\text{ }13504}\\ 16965&\big|\text{ }\text{ }\text{ }\text{ }89600\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }84825}\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{8.49m}} \end{align*}
4)	\begin{align*} &x^2=729\\[5pt] &x=\sqrt{729}\\[5pt] &x=3^3\\[5pt] &=\underline{\underline{27^{th} term}} \end{align*}	\begin{align*} &\text{ }\text{ }\\ 3 &\big|{729}\\ 3 &\big|\overline{243}\\ 3 &\big|\overline{81}\\ 3 &\big|\overline{27}\\ 3 &\big|\overline{9}\\ 3 &\big|\overline{3}\\ &\big|\overline{1}\\ \end{align*}

By studying this lesson you will be able to

Use the division method to find an approximate value for the square root of a positive number which is not a prefect square.