Question

Find the value of ${\left(103\right)}^2$ using algebraic identities.

• A. 10609
• B. 10906
• C. 10069
• D. 16009

Answer 1

The correct option is A

10609

We need to find the square of 103. For that, we split it into 2 numbers whose squares are easy to calculate.

Hence, we write ${\left(103\right)}^2$ as ${(100+3)}^2$.

We have ${(a+b)}^2=a^2+b^2+2ab$

Comparing it with the above identity, we have $a=100,b=3$

On expanding, we get ${\left(100\right)}^2+{\left(3\right)}^2+2\left(100\right)\left(3\right)=10000+9+600=10609$