Question

Find the square of 32 without multiplication.
A. 32768
B. 1024
C. 992
D. 31744

Answer 1

Hint: We know that the square of a number will be found by multiplying the number by itself. In this particular question we will find the square of a number without multiplication by using the algebraic formula ${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$.

Complete step by step answer:
We have to find the square of 32 without multiplication.
We know that when we multiply a number by itself we will get the square of that number.
For example if we have a number n and we have to find the square then we can write it as
$\Rightarrow n\times n={{n}^{2}}$
Now, we know that we can write 32 as $\left( 30+2 \right)$
So the square of 32 without multiplication will be
$\begin{align}
  & \Rightarrow {{\left( 32 \right)}^{2}} \\
 & \Rightarrow {{\left( 30+2 \right)}^{2}} \\
\end{align}$
Now, we know that we have an algebraic formula which is given as ${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$.
So by applying the formula in the above obtained equation we will get
$\Rightarrow {{\left( 30 \right)}^{2}}+{{2}^{2}}+2\times 30\times 2$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow 900+4+120 \\
 & \Rightarrow 1024 \\
\end{align}$
Hence we get the square of 32 without multiplication as 1024.

So, the correct answer is “Option B”.

Note: The point to be remembered is that always try to break the number into multiples of 10. For example if we have a number like 29 then we can write it as $\left( 30-1 \right)$ and find the square by using the algebraic formula ${{\left( a-b \right)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab$. Alternatively we can also use a shortcut trick to find the square of a number.