Basic Maths: Test 59

$\begin{align} & \,\,\sqrt{1225}\times \frac{35}{100}\div 0.01={{\left( ? \right)}^{2}}\div 16 \\ & \Rightarrow 35\times \frac{35}{100}\times 100=\frac{{{?}^{2}}}{16} \\ & \Rightarrow {{?}^{2}}=35\times 35\times 16 \\ & ={{35}^{2}}\times {{4}^{2}} \\ & =?=35\times 4=140 \\ \end{align}$

$\begin{align} & If\,\,225=a\,\,and\,\,\,121=b,\,\,then \\ & Expression \\ & =\frac{{{a}^{2}}-{{b}^{2}}}{a-b} \\ & \left[ a-b=225-121=104 \right] \\ & =\frac{\left( a+b \right)\left( a-b \right)}{\left( a-b \right)}=a+b \\ & =225+121 \\ & =350 \\ \end{align}$

$\begin{align} & =3\sqrt{63}-6\sqrt{\frac{7}{36}}-\sqrt{112} \\ & =3\sqrt{9\times 7}-\sqrt{\frac{7\times 6\times 6}{6\times 6}}-\sqrt{16\times 7} \\ & =3\times 3\sqrt{7}-\sqrt{7}-4\sqrt{7}=4\sqrt{7} \\ \end{align}$

$\begin{align} & ={{\left( 7.3+2.7 \right)}^{2}} \\ & \left[ {{a}^{2}}+2ab+{{b}^{2}}={{\left( a+b \right)}^{2}} \right] \\ & ={{10}^{2}} \\ & =100 \\ \end{align}$

$\begin{align} & Let\,\,2.56=a\,\,and\,\,1.28=b \\ & Therefore\,\,\exp ression \\ & =\frac{{{a}^{3}}-{{b}^{3}}}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =\frac{\left( a-b \right)\left( {{a}^{2}}+ab+b \right)}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =a-b=2.56-1.28=1.28 \\ \end{align}$