Question

Evaluate the following: ${\left( {0.98} \right)^2}$
A) 0.9664
B) 0.9604
C) 0.9864
D) 0.9964

Answer 1

Hint:
We are asked in the question to Evaluate ${\left( {0.98} \right)^2}$ .
Since, we will split 0.98 as 1-0.02. After that, by applying the formula ${\left( {a - b} \right)^2} = {a^2} - 2ab - {b^3}$ on the above equation i.e. 1-0.2
Thus, solving further we will get the required answer.

Complete step by step solution:
We are asked in the question to Evaluate ${\left( {0.98} \right)^2}$ .
Since, we can split 0.98 as 1-0.02.
Therefore, we can write ${\left( {0.98} \right)^2}$ as ${\left( {1 - 0.02} \right)^2}$ .
 $ = {\left( {1 - 0.02} \right)^2}$
Now, applying the formula ${\left( {a - b} \right)^2} = {a^2} - 2ab - {b^2}$ on the above equation, we get,
 $ = {\left( 1 \right)^2} - 2\left( 1 \right)\left( {0.02} \right) - {\left( {0.02} \right)^2}$
$=1-0.04-0.0004 \\
=1-0.0396 \\
=0.9604$
Hence, ${\left( {0.98} \right)^2} = 0.9604$ .

Therefore, the option (B) is correct.

Note:
Some other useful formulas:
1) $\left( {{a^2} - {b^2}} \right) = \left( {a + b} \right)\left( {a - b} \right)$
2) $\left( {{a^2} + {b^2}} \right) = {\left( {a + b} \right)^2} - 2ab$
3) ${\left( {a - b} \right)^2} = {a^2} - 2ab - {b^2}$
4) ${\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}$