Question

Find the value of $(76{)}^2$ by visualizing the identity $(a+b{)}^2=a^2+2ab+b^2$.

• A. $7,765$
• B. $7,655$
• C. $5,776$
• D. $6,675$

Answer 1

The correct option is C $5,776$

We have to find value of $(76{)}^2$. So, Let us visualize this with the help of diagram.


$76$ can also be written as $(70+6)$.

So, the value of $(76{)}^2$ will be area of square ABCD.

$\Rightarrow$Area of square ABCD $=(70+6)(70+6)=(70+6{)}^2$sq.units.

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

Brown and green rectangles have similar dimensions.
So, area of brown and green rectangles $=(70\times 6)$ sq.units.

Area of white square is $=(6\times 6)$ sq.units.

And, Area of yellow square $=(70\times 70)$ sq.units

Now, $\Rightarrow (70+6{)}^2=70\times 70+70\times 6+70\times 6+6\times 6)$

$\Rightarrow (70+6{)}^2=(70{)}^2+2\times 70\times 6+6^2$

$\Rightarrow (70+6{)}^2=4,900+840+36=5,776.$sq.units.

$\Rightarrow (76{)}^2=5,776$

$\therefore$ Required value of $(76{)}^2$ is $5,776$.