Question

Find the value of ${249^2} - {248^2}$ is
$A)1$
$B)477$
$C)487$
$D)497$

Answer 1

Hint: Squaring a number means multiplying the number by itself, i.e., multiplying a number two times. If we have to find out the value of “a” squared then we will just multiply ‘a ‘by ‘a ‘. The squared term is usually pronounced as a times a.
Thus, a squared = \[a \times a = {a^2}\]. The commonly used symbol for a square is \[{a^2}\]. Here ‘a’ is known as the ‘base’ while the power 2 is known as ‘exponent ‘. For example,
If we have to find the value of \[20\] squared then we will multiply \[20\] by itself which means
\[20\] squared = \[{20^2}\]\[\; = {\text{ }}20 \times 20{\text{ }} = {\text{ }}400\] Here \[20\] is the base and $2$ is exponent.

Complete step by step solution:
To calculate the square of ${249^2} - {248^2}$ we have to multiply $(249 \times 249) - (248 \times 248)$ by itself
Since multiplicand refers to the number multiplied. Also, multiplier refers to the number that multiplies the first number. Have a look at an example; while multiplying $5 \times 7$the number $5$ is called the multiplicand and the number $7$is called the multiplier.
Thus $249$ Squared \[249 \times 249 = 62001\] . (by the multiplication operation)
Also, the $248$ Squared \[248 \times 248 = 61504\] . (by the multiplication operation)
Hence using the subtraction operation operations, we get ${249^2} - {248^2} = 62001 - 61504$ and thus we get
${249^2} - {248^2}
= 62001 - 61504
= 497$
Therefore, the option $D)497$ is correct.

So, the correct answer is “Option D”.

Note: The above problem can also be solved by using a standard algebraic formula that is ${a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$ . Take a look at the given question ${249^2} - {248^2}$ as we can see that this is in the form of ${a^2} - {b^2}$ where $a = 249$ and $b = 248$ . Now let us solve this by using the formula, here it is given that ${249^2} - {248^2}$ by using the formula ${a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$ we can write it as ${249^2} - {248^2} = \left( {249 + 248} \right)\left( {249 - 248} \right)$
On simplifying the above, we get
${249^2} - {248^2} = \left( {497} \right)\left( 1 \right) = 497$
Thus, we got the answer.