Question

Part A: The decimal form of the rational number 3/40 is

Answer 1

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c | } \\ \bf{Part \: A} & \bf \footnotesize{The \: decimal \: form \: of \: the \: rational \: number \: \dfrac{3}{40} \: is \: \gray{ \normalsize{ 0.075 }}} \\ \\ \hline \\ \bf{Part \: B}& \: \bf \footnotesize{The \: value \: of \: \dfrac{1}{ \sqrt[4]{(9)^{ - 2} } } \: is \: \normalsize 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \hline \\ { \bf Part \:C \: }& \: { \bf\footnotesize{On \: simplifying \: \: (5+3 \sqrt{7} ) + (12 - 3 \sqrt{7}) \: we \: get \: \normalsize{ 17 }. \: \: \: \: \: \: \: \: }} \\ \\ \end{array}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\bf \underline{Answer-}$

${ \bf{Part \: A \: | \: \footnotesize{The \: decimal \: form \: of \: the \: rational \: number \: \dfrac{3}{40} \: is \: \gray{ \normalsize{ 0.075 }}}}}$

${ \bf{Part \: B \: | \: \footnotesize{The \: value \: of \: \dfrac{1}{ \sqrt[4]{(9)^{ - 2} } } \: is \: \normalsize 3 }}}$

$\bf \underline{Step \:by \:step\: Explanation-}$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ \sqrt[4]{(9)^{ - 2} } }}$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ \sqrt[ \cancel4]{(9)^{ \cancel{ - 2}} } }}$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ \sqrt{9^{ - 1} } }}$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ {3}^{ - 1 } }}$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ \dfrac{1}{3} }}$

${ \sf \: \: \: \: \: : \: \: \implies3}$

${ \bf Part \:C \: } | \: { \bf\footnotesize{On \: simplifying \: \: (5+3 \sqrt{7} ) + (12 - 3 \sqrt{7}) \: we \: get \: \normalsize{ 17 }. }}$

${~~~\sf ~~:~~\implies (5+3 \sqrt{7} ) + (12 - 3 \sqrt{7})}$

${~~~~\sf ~:~~\implies 5+ \cancel{3 \sqrt{7}} + 12 \cancel{ - 3 \sqrt{7}}}$

${~\sf ~~~~:~~\implies 17}$

$\underline{\rule{200pt}{2.5pt}}$