Question

Q 5 please helpme guy ​

Answer 1

To find :

Squares of :-

$\sf{ (a) \: 199} \\ \sf{ (b) \: 103} \\ \sf{ (c) \: 202} \\ \sf{ (d) \: 395} \\ \sf{ (e) \: 995}$

Formula to be used :

$\sf{ \bullet \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} } \\ \\ \sf{ \bullet \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }$

Solution:

a) Identity used :

$\sf{ \bullet \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }$

$\sf \red{ {(199)}^{2} } \\ \\ \sf { \longrightarrow {(200 - 1)}^{2} } \\ \\ \sf { \longrightarrow {200}^{2} - (2 \times 200 \times 1) + {1}^{2} } \\ \\ \sf { \longrightarrow 40000 - 400 + 1 } \\ \\ \sf { \longrightarrow 39600 + 1 } \\ \\ \sf \red { \longrightarrow 39601 }$

_______________________________

b) Identity used:

$\sf{ \bullet \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }$

$\sf \red{ {(103)}^{2} } \\ \\ \sf { \longrightarrow {(100 + 3)}^{2} } \\ \\ \sf { \longrightarrow {100}^{2} + (2 \times 100 \times 3) + {3}^{2} } \\ \\ \sf { \longrightarrow 10000 + 600 + 9 } \\ \\ \sf { \longrightarrow 10600 + 9 } \\ \\ \sf \red { \longrightarrow 10609 }$

_______________________________

c) Identity used :

$\sf{ \bullet \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }$

$\sf \red{ {(202)}^{2} } \\ \\ \sf { \longrightarrow {(200 + 2)}^{2} } \\ \\ \sf { \longrightarrow {200}^{2} + (2 \times 200 \times 2) + {2}^{2} } \\ \\ \sf { \longrightarrow 40000 + 800 + 4 } \\ \\ \sf { \longrightarrow 40800 + 4 } \\ \\ \sf \red { \longrightarrow 408004 }$

_______________________________

d) Identity used :

$\sf{ \bullet \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }$

$\sf \red{ {(395)}^{2} } \\ \\ \sf { \longrightarrow {(400 - 5)}^{2} } \\ \\ \sf { \longrightarrow {400}^{2} - (2 \times 400 \times 5) + {5}^{2} } \\ \\ \sf { \longrightarrow 160000 - 4000 + 25 } \\ \\ \sf { \longrightarrow 156000 + 25 } \\ \\ \sf \red { \longrightarrow 156025 }$

________________________________

e) Identity used :

$\sf{ \bullet \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }$

$\sf \red{ {(998)}^{2} } \\ \\ \sf { \longrightarrow {(1000 - 2)}^{2} } \\ \\ \sf { \longrightarrow {1000}^{2} - (2 \times 1000 \times 2) + {2}^{2} } \\ \\ \sf { \longrightarrow 1000000 - 4000 + 4 } \\ \\ \sf { \longrightarrow 996000 + 4 } \\ \\ \sf \red { \longrightarrow 996004 }$

_______________________________

Know more!

• Squares of odd numbers are always odd.

• Squares of even numbers are always even.

• Any number ending with 2,8,3 or 7 is never a perfect square.

• For every natural number, n > 1, $\sf { 2n, {n}^{2} - 1, {n}^{2} +1 }$ is a pythagorean triplet.