Question

The value of $(810{)}^2$ by visualizing the identity $(a+b{)}^2=a^2+2ab+b^2$ is .

Answer 1

We have to find value of $(810{)}^2$. So, let us visualize this with the help of diagram.


$810$ can also be written as $(800+10)$.

So, the value of $(810{)}^2$ will be area of square PQRS.

$\Rightarrow$Area of square PQRS $=(800+10)(800+10)=(800+10{)}^2$sq.units.

It can also be written as
Area of square PQRS = Area of Red square + Area of Orange and White rectangles + Area of Blue square

Orange and white rectangles have similar dimensions.
So, area of orange and white rectangles $=(800\times 10)$ sq.units.

Area of blue square is $=(10\times 10)$ sq.units.

And, Area of red square $=(800\times 800)$ sq.units

Now, $\Rightarrow (800+10{)}^2=800\times 800+800\times 10+800\times 10+10\times 10)$
$\Rightarrow (800+10{)}^2=(800{)}^2+2\times 800\times 10+{10}^2$
$\Rightarrow (800+10{)}^2=6,40,000+16,000+100=6,56,100.$sq.units.
$\Rightarrow (810{)}^2=6,56,100$
$\therefore$ Required value of $(810{)}^2$ is $656,100$.