Question

The value of $(908{)}^2$ by visualizing the identity $(a+b{)}^2=a^2+2ab+b^2$ is .

Answer 1

We have to find value of $(908{)}^2$. So, let us visualize this with the help of diagram.


$908$ can also be written as $(900+8)$.

So, the value of $(908{)}^2$ will be area of square ABCD.

$\Rightarrow$Area of square ABCD $=(900+8)(900+8)=(900+8{)}^2$sq.units.

It can also be written as
Area of square ABCD = Area of Yellow square+Area of Black and Green rectangles + Area of Blue square

Black and green rectangles have similar dimensions.
So, area of Black and Green rectangles $=(900\times 8)$ sq.units.

Area of blue square is $=(8\times 8)$ sq.units.

And, Area of yellow square $=(900\times 900)$ sq.units

Now, $\Rightarrow (900+8{)}^2=900\times 900+900\times 8+900\times 8+8\times 8)$
$\Rightarrow (900+8{)}^2=(900{)}^2+2\times 900\times 8+8^2$
$\Rightarrow (900+8{)}^2=8,10,000+14,400+64=8,24,464.$sq.units.
$\Rightarrow (908{)}^2=8,24,464$
$\therefore$ Required value of $(908{)}^2$ is $824,464$.