Question

Find the value of ${97}^2$ using algebraic identities.

• A. 9904
• B. 9049
• C. 9409
• D. 9490

Answer 1

The correct option is C 9409

We need to find the square of 97. For that, we split it into 2 numbers whose squares are easy to calculate.

Hence, we write ${\left(97\right)}^2$ 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 ${\left(100\right)}^2+{\left(3\right)}^2-2\left(100\right)\left(3\right)=10000+9-600=9409$