Question

The difference of the squares \[\left( {{61}^{2}}-{{51}^{2}} \right)\] is equal to?

Answer 1

Hint: For solving this question you should know about the square of any value. The square of any value is equal to the \[{{2}^{nd}}\] ordered or the 2 powers of that value. Which directly means that the same value will multiply by itself for one time. Which is known as a square of any value.

Complete step by step answer:
In our question it is asked to calculate the square of 61 and 51 and then the difference of them. So, for calculating the square of any number we will multiply that by the same number. For any number square means \[{{2}^{nd}}\] power of that number.
If the given number for which we have to calculate the square is big then we divide it between two parts and the parts are like as if if we add them then the desired number will occur again. So, generally we divide it with a near whole square value, whose square is known or easy to calculate the square of both of the parts.
We divide them in the addition form like a + b or we divide them in the subtraction form a – b. And both the numbers a & b are easy for calculating the square of this number.
So, first we have to calculate the squares of 61 and 51.
So, the square of \[61=61\times 61\]
                                     \[=3721\]
Square of \[51=51\times 51\]
                         \[=2601\]
So, the difference of both of this is \[={{\left( 61 \right)}^{2}}-{{\left( 51 \right)}^{2}}\]
                                                                \[\begin{align}
  & =3721-2601 \\
 & =1120 \\
\end{align}\]
So, the difference of the squares \[\left( {{61}^{2}}-{{51}^{2}} \right)\] is equal to 1120.

Note: We can solve this problem using algebraic identity as $a^2-b^2=(a-b)(a+b)$
For calculating the square of any value by the division method you should divide your number in two parts as in a way that the calculation for the square will be easy and it will be possible if we subtract or add any number in the nearly present square numbers or the known square of any number. But you should be careful when calculating the square of something by this method because there can be some mistakes during calculation in this.