Question

Can u answer all Grade 9 Chapter Numbers ​

Answer 1

Solution :

$1) \: \sf \: (7 + \sqrt{2} )^{2}$

Using the identity :

$\bigstar\: \boxed{ \sf \: (a + b)^{2} = {a}^{2} + 2ab + {b}^{2}}$

$\longrightarrow \sf ({7})^{2} + 2(7)( \sqrt{2} ) + ( { \sqrt{2}) }^{2}$

$\longrightarrow \sf 49 + 14 \sqrt{2} + 2$

$\longrightarrow \red{\sf 51 + 14 \sqrt{2}}$

________________________________

$\sf \: 2) \: (\sqrt{3} - \sqrt{2} )( \sqrt{3} + \sqrt{2} )$

Using the identity :

$\bigstar\: \boxed{ \sf \: (a + b)(a - b) = {a}^{2} - {b}^{2} }$

$\longrightarrow \sf ( \sqrt{3} ) ^{2} - ( { \sqrt{2} )}^{2}$

$\longrightarrow \sf ( \sqrt{3} \times \sqrt{3} ) - ( \sqrt{2} \times \sqrt{2} )$

$\longrightarrow \sf 3 - 2$

$\longrightarrow \red{ \sf \:1 }$

________________________________

$\sf \: 3) \: (1+ \sqrt{2} )( 1 - \sqrt{2} )$

Using the identity :

$\bigstar\: \boxed{ \sf \: (a + b)(a - b) = {a}^{2} - {b}^{2} }$

$\longrightarrow \sf ({1})^{2} - ( { \sqrt{2} )}^{2}$

$\longrightarrow \sf (1 \times 1) - (\sqrt{2} \times \sqrt{2} )$

$\longrightarrow \sf 1 - 2$

$\longrightarrow \red{ \sf \: - 1 }$

________________________________

$4) \: \sf \: ( \sqrt{7} - \sqrt{11} )^{2}$

Using the identity :

$\bigstar\: \boxed{ \sf \: (a - b)^{2} = {a}^{2} - 2ab + {b}^{2}}$

$\longrightarrow \sf ( { \sqrt{7}) }^{2} - 2( \sqrt{7} )( \sqrt{11} ) + (\sqrt{11} )^{2}$

$\longrightarrow \sf 7 - 2( \sqrt{7} ) (\sqrt{11} ) + 11$

$\longrightarrow\red{ \sf\: 18 - 2 \sqrt{77}}$