1)i	\begin{align} &{676}\\[5pt] \end{align} \begin{align} &\text{ }\text{ }26\\ 2 &\big|\overline{676}\\ &\big|\underline{4}\\ 46&\big|276\\ &\big|\underline{276}\\ &\big|\text{ }\text{ }00\\ = \text{ }\text{ }&\underline{\underline{26}}\\ \text{ }\\ \end{align}	ii	\begin{align} &{1024}\\[5pt] \end{align} \begin{align} &\text{ }\text{ }32\\ 3 &\big|\overline{1024}\\ &\big|\underline{\text{ }\text{ }9}\\ 62&\big|\text{ }\text{ }124\\ &\big|\underline{\text{ }\text{ }124}\\ &\big|\text{ }\text{ }\text{ }\text{ }00\\ = \text{ }\text{ }&\underline{\underline{32}}\\ \text{ }\\ \end{align}	iii	\begin{align} &{2209}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }47\\ 4 &\big|\overline{2209}\\ &\big|\underline{16}\\ 87&\big|\text{ }\text{ }609\\ &\big|\underline{\text{ }\text{ }609}\\ &\big|\text{ }\text{ }\text{ }\text{ }00\\ = \text{ }\text{ }&\underline{\underline{47}}\\ \end{align*}
iv	\begin{align} &{2809}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }53\\ 5 &\big|\overline{2809}\\ &\big|\underline{25}\\ 103&\big|\text{ }\text{ }309\\ &\big|\underline{\text{ }\text{ }309}\\ &\big|\text{ }\text{ }\text{ }\text{ }00\\ = \text{ }\text{ }&\underline{\underline{53}} \end{align*}	v	\begin{align} &{3721}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }61\\ 6 &\big|\overline{3721}\\ &\big|\underline{36}\\ 121&\big|\text{ }\text{ }121\\ &\big|\underline{\text{ }\text{ }121}\\ &\big|\text{ }\text{ }\text{ }\text{ }00\\ = \text{ }\text{ }&\underline{\underline{61}} \end{align*}
2a)i	\begin{align} &\sqrt{8}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }2.82\\ 2 &\big|\overline{8}\\ &\big|\underline{4}\\ 48&\big|400\\ &\big|\underline{384}\\ 562&\big|\text{ }\text{ }1600\\ &\big|\underline{\text{ }\text{ }1124}\\ &\big|\text{ }\text{ }\text{ }\text{ }476\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{2.8}} \end{align*}	ii	\begin{align} &\sqrt{19}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }4.35\\ 4 &\big|\overline{19}\\ &\big|\underline{16}\\ 83&\big|\text{ }\text{ }300\\ &\big|\underline{\text{ }\text{ }249}\\ 865&\big|\text{ }\text{ }\text{ }\text{ }5100\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }4325}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }775\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{4.4}} \end{align*}	iii	\begin{align} &\sqrt{26}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }5.09\\ 5 &\big|\overline{26}\\ &\big|\underline{25}\\ 100&\big|\text{ }\text{ }100\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }0}\\ 1009&\big|\text{ }\text{ }\text{ }10000\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }9081}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }919\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{5.1}} \end{align*}
iv	\begin{align} &\sqrt{263}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }16.21\\ 1 &\big|\overline{263}\\ &\big|\underline{1}\\ 26&\big|163\\ &\big|\underline{156}\\ 322&\big|\text{ }\text{ }\text{ }\text{ }700\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }644}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }5600\\ 3241&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }3241\\ &\big|\overline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\\2359}\\ \approx \text{ }\text{ }&\underline{\underline{16.2}} \end{align*}	v	\begin{align} &\sqrt{2745}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }\text{ }\text{ }52.39\\ 5 &\big|\overline{2745}\\ &\big|\underline{25}\\ 102&\big|\text{ }\text{ }245\\ &\big|\underline{\text{ }\text{ }204}\\ 1043&\big|\text{ }\text{ }\text{ }\text{ }4100\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }3129}\\ 10469&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }97100\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }94221}\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{52.4}} \end{align*}	vi	\begin{align} &\sqrt{3630}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }\text{ }\text{ }60.24\\ 6 &\big|\overline{3630}\\ &\big|\underline{36}\\ 120&\big|\text{ }\text{ }030\\ &\big|\underline{\text{ }\text{ }0}\\ 1202&\big|\text{ }\text{ }\text{ }\text{ }3000\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }2404}\\ 12044&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }59600\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }48176}\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{60.2}} \end{align*}
2b)i	\begin{align} &\sqrt{5.4}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }2.32\\ 2 &\big|\overline{5.40}\\ &\big|\underline{4}\\ 43&\big|140\\ &\big|\underline{129}\\ 462&\big|\text{ }\text{ }1100\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }924}\\ &\big|\text{ }\text{ }\text{ }\text{ }176\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{2.3}} \end{align*}	ii	\begin{align} &\sqrt{3.45}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }1.85\\ 1 &\big|\overline{3.45}\\ &\big|\underline{1}\\ 28&\big|245\\ &\big|\underline{224}\\ 365&\big|\text{ }\text{ }2100\\ &\big|\underline{\text{ }\text{ }1825}\\ &\big|\text{ }\text{ }\text{ }\text{ }275\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{1.9}} \end{align*}	iii	\begin{align} &\sqrt{15.3}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }3.91\\ 3 &\big|\overline{15.3}\\ &\big|\underline{\text{ }\text{ }9}\\ 69&\big|\text{ }\text{ }630\\ &\big|\underline{\text{ }\text{ }621}\\ 78&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }900\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }781}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }119\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{3.9}} \end{align*}
iv	\begin{align} &\sqrt{243.2}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }15.59\\ 1 &\big|\overline{243.20}\\ &\big|\underline{1}\\ 25&\big|143\\ &\big|\underline{125}\\ 305&\big|\text{ }\text{ }1820\\ &\big|\underline{\text{ }\text{ }1525}\\ &\big|\text{ }\text{ }\text{ }\text{ }29500\\ 3109&\big|\text{ }\text{ }\text{ }\text{ }27981\\ &\big|\overline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\\1519}\\ \approx \text{ }\text{ }&\underline{\underline{15.6}} \end{align*}	v	\begin{align} &\sqrt{4061.3}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }63.72\\ 6 &\big|\overline{4061.30}\\ &\big|\underline{36}\\ 123&\big|\text{ }\text{ }\text461\\ &\big|\underline{\text{ }\text{ }369}\\ 1267&\big|\text{ }\text{ }\text{ }\text{ }9230\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }8869}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }36100\\ 12742&\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }25484}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }10616\\ \approx \text{ }\text{ }&\underline{\underline{63.7}} \end{align*}	vi	\begin{align} &\sqrt{85.124}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }\text{ }\text{ }9.22\\ 9 &\big|\overline{85.1240}\\ &\big|\underline{81}\\ 182&\big|\text{ }\text{ }412\\ &\big|\underline{\text{ }\text{ }364}\\ 1842&\big|\text{ }\text{ }\text{ }\text{ }4840\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }3684}\\ &\big|\text{ }\text{ }\text{ }\text{ }1156\\ \text{ }\\ \approx \text{ }\text{ }&\underline{\underline{9.2}} \end{align*}
vii	\begin{align} &\sqrt{0.0064}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }0.08\\ 0 &\big|\overline{0.0064}\\ &\big|\underline{0}\\ 0&\big|000\\ &\big|\underline{\text{ }\text{ }00}\\ 8&\big|\text{ }\text{ }\text{ }\text{ }064\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }64}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }0\\ \text{ }\\ \text{ }\text{ }&\underline{\underline{0.08}} \end{align*} \begin{align*} \approx \text{ }\text{ }&\underline{\underline{0.1}} \end{align*}	viii	\begin{align} &\sqrt{0.000144}\\[5pt] \end{align} \begin{align*} &\text{ }\text{ }0.012\\ 0 &\big|\overline{0.000144}\\ &\big|\underline{0}\\ 0&\big|000\\ &\big|\underline{\text{ }\text{ }00}\\ 1&\big|\text{ }\text{ }\text{ }\text{ }001\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }01}\\ 22&\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }0.44\\ &\big|\underline{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }0.44}\\ &\big|\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }0\\ \text{ }\\ \text{ }\text{ }&\underline{\underline{0.012}} \end{align*} \begin{align*} \approx \text{ }\text{ }&\underline{\underline{0.0}} \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.