Question

What is 23 squared?

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 \[{{2}^{\circ }}\] power 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 23.
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 that if we add them then the desired number will occur again. So, generally we divide it with the 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 decide them in the subtraction form \[a-b\]. And both the numbers a & b are easy for calculating the square of this number.
By this method we can calculate the square of same with writing \[23=25-2\]: -
Our number for being squared is 23.
We can write 23 as 25 – 2
\[\Rightarrow 23=25-2\]
Since, we know that, \[{{\left( a-b \right)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}\Rightarrow {{\left( 23 \right)}^{2}}={{\left( 25-2 \right)}^{2}}\]
\[\begin{align}
  & \Rightarrow {{\left( 23 \right)}^{2}}={{\left( 25 \right)}^{2}}-2\left( 2 \right)\left( 25 \right)+{{\left( 2 \right)}^{2}} \\
 & \Rightarrow {{\left( 23 \right)}^{2}}=625-100+4 \\
 & \Rightarrow {{\left( 23 \right)}^{2}}=529 \\
\end{align}\]
Therefore, the square of 23 is 529.

Note: Alternate method:
So, we have to calculate the square of 23.
\[x=23\]
Square of any value \[={{x}^{2}}\]
\[\Rightarrow {{x}^{2}}=x.x\]
\[\begin{align}
  & \Rightarrow {{\left( 23 \right)}^{2}}=23.23 \\
 & \Rightarrow {{\left( 23 \right)}^{2}}=529 \\
\end{align}\]
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 number or the known square of any number. But you should be careful for calculating the square of something by this method because there can be some mistakes during calculation in this.