Question

9 si 10 va rog urgent

Answer 1

$9.~a)~\sqrt{108} \\\\ \left\begin{array}{ccc}108\\~54\\~27\\~~9\\~~3\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\3\\3\\3\\\\\end{array}\right~~~ \Rightarrow \sqrt{108} =6\sqrt{3} \left\begin{array}{ccc}\end{array}\right$

$b)~\sqrt{112} \\\\ \left\begin{array}{ccc}112\\~56\\~28\\~14\\~~7\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\2\\2\\7\\\\\end{array}\right ~~~\Rightarrow \sqrt{112} =4\sqrt{7}$

$c)~\sqrt{125} \\\\ \left\begin{array}{ccc}125\\~25\\~~5\\~~1\end{array}\right| \left\begin{array}{ccc}5\\5\\5\\\\\end{array}\right ~~~\Rightarrow \sqrt{125} =5\sqrt{5}$

$d)~\sqrt{128} \\\\ \left\begin{array}{ccc}128\\~64\\~32\\~16\\~~8\\~~4\\~~2\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\2\\2\\2\\2\\2\\\\\end{array}\right~~~ \Rightarrow \sqrt{128} =8\sqrt{2}$

$e)~\sqrt{150} \\\\ \left\begin{array}{ccc}150\\~75\\~25\\~~5\\~~1\end{array}\right| \left\begin{array}{ccc}2\\3\\5\\5\\\\\end{array}\right ~~~ \Rightarrow \sqrt{150} =5\sqrt{6}$

$f)~\sqrt{175}\\\\ \left\begin{array}{ccc}175\\~35\\~~7\\~~1\end{array}\right| \left\begin{array}{ccc}5\\5\\7\\\\\end{array}\right ~~~\Rightarrow \sqrt{175} =5\sqrt{7}$

$g)~\sqrt{180}\\\\ \left\begin{array}{ccc}180\\~90\\~45\\~15\\~~5\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\3\\3\\5\\\\\end{array}\right ~~~\Rightarrow \sqrt{180} =6\sqrt{5}$

$h)~\sqrt{192}\\\\ \left\begin{array}{ccc}192\\~96\\~48\\~24\\~12\\~~6\\~~3\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\2\\2\\2\\2\\3\\\\\end{array}\right ~~~\Rightarrow \sqrt{192} =8\sqrt{3}$

$10.~a)~\sqrt{245} \\\\ \left\begin{array}{ccc}245\\~49\\~~7\\~~1\end{array}\right| \left\begin{array}{ccc}5\\7\\7\\\\\end{array}\right ~~~\Rightarrow \sqrt{245} =7\sqrt{5}$

$b)~\sqrt{300} \\\\ \left\begin{array}{ccc}300\\150\\~75\\~25\\~~5\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\3\\5\\5\\\\\end{array}\right ~~~\Rightarrow \sqrt{300} =10\sqrt{3}$

$c)~\sqrt{320} \\\\ \left\begin{array}{ccc}320\\160\\~80\\~40\\~20\\~10\\~~5\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\2\\2\\2\\2\\5\\\\\end{array}\right ~~~\Rightarrow \sqrt{320} =8\sqrt{5}$

$d)~\sqrt{252} \\\\ \left\begin{array}{ccc}252\\126\\~63\\~21\\~~7\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\3\\3\\7\\\\\end{array}\right ~~~\Rightarrow \sqrt{252} =6\sqrt{7}$

$e)~\sqrt{720} \\\\ \left\begin{array}{ccc}720\\360\\180\\~90\\~45\\~15\\~~5\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\2\\2\\3\\3\\5\\\\\end{array}\right ~~~\Rightarrow \sqrt{720}=12\sqrt{5}$

$f)~\sqrt{588} \\\\ \left\begin{array}{ccc}588\\294\\147\\~49\\~~7\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\3\\7\\7\\\\\end{array}\right ~~~\Rightarrow \sqrt{588} =14\sqrt{3}$

$g)~\sqrt{675}\\\\ \left\begin{array}{ccc}675\\225\\~75\\~25\\~~5\\~~1\end{array}\right| \left\begin{array}{ccc}3\\3\\3\\5\\5\\\\\end{array}\right ~~~ \Rightarrow \sqrt{675}=15\sqrt{3}$

$h)~\sqrt{648}\\\\ \left\begin{array}{ccc}648\\324\\162\\~81\\~27\\~~9\\~~3\\~~1\end{array}\right| \left\begin{array}{ccc}2\\2\\2\\3\\3\\3\\3\\\\\end{array}\right ~~~\Rightarrow \sqrt{648} =18\sqrt{2}$