Question

find the square of 56 and 79 using identity.
CLASS 8
Chapter-Squares and Square roots​

Answer 1

In Accordance to Class 8th, We can use following Algebriac identities :

• $\rm {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$
• $\rm {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$
• $\rm(a + b)(a - b) = {a}^{2} - {b}^{2}$
• $\rm (x + a)(x + b) = {x}^{2} + (a + b)x + ab$

Thus,

• For squaring 56 & 79 (with usage of above mentioned algebraic identities), we need to transform these numbers as sum or difference of two numbers.

$\therefore \: \: \: \: 56 = 50 + 6 \: \: \: \: \\ \: \: \: \: \: \: \: \: 79 = 80 - 1$

Now,

• Performing calculation,

${(56)}^{2} = {(50 + 6)}^{2} \\ \boxed{ \small\textsf{Here, We can use the identity}{ \: \: \rm{(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab} \: \: } \\ \: \: \: \: \: = > {(50)}^{2} + {(6)}^{2} + 2(50)(6) \\ \: \: \: \: \: = > 2500 + 36 + 600 \\ \: \: \: \: \: = > \red{3136}$

And,

${(79)}^{2} = {(80 - 1)}^{2} \\ \boxed{ \small\textsf{Here, We can use the identity}{ \: \: \rm{(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab} \: \: } \\ \: \: \: \: \: \: = > {(80)}^{2} + {(1)}^{2} - 2(1)(80) \\ \: \: \: \: \: \: = > 6400 + 1 - 160 \\ \: \: \: \: \: \: = > 6401 - 160 \\ \: \: \: \: \: \: = > \red{6241}$

Hence,

• Square of 56 is 3136.
• Square of 79 is 6241.

Answer 2

Answer has been attached here.

Hope it helps you.