Question

Value of ${{\left( 62 \right)}^{2}}$ is: -
(a) 124
(b) -124
(c) 3244
(d) 3844

Answer 1

Hint: Assume the value of the given expression as E. Now, write the base number 62 as the sum of two numbers 60 and 2. Use the algebraic identity ${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$ and substitute the value a = 60 and b = 2 to expand the terms. Perform simple addition to get the answer.

Complete step-by-step solution:
Here we have been provided with the expression ${{\left( 62 \right)}^{2}}$ and we are asked to find its value. Here we will use the suitable algebraic identity to get the value. Assuming the given expression as E we have,
$\Rightarrow E={{\left( 62 \right)}^{2}}$
Now, we can write the base number which is 62 as the sum of two numbers which are 60 and 2, so we get,
$\Rightarrow E={{\left( 60+2 \right)}^{2}}$
We know that the whole square formula of the sum of two numbers is given as ${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$, so considering a = 60 and b = 2 we get,
$\begin{align}
  & \Rightarrow E={{\left( 60 \right)}^{2}}+{{2}^{2}}+2\left( 60 \right)\left( 2 \right) \\
 & \Rightarrow E=3600+4+240 \\
\end{align}$
Performing simple addition to simplify we get,
$\therefore E=3844$
Hence, option (d) is the correct answer.

Note: Note that 62 is a large number and it is somewhat difficult to calculate its square directly therefore we have broken it into 60 + 2 because it is relatively easy to calculate the square values of 60 and 2. You must remember the other two important algebraic identities given as
${{\left( a-b \right)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab$ and $\left( {{a}^{2}}-{{b}^{2}} \right)=\left( a-b \right)\left( a+b \right)$. In addition to these we also have certain algebraic identities involving the cube of numbers that must be remembered like ${{\left( a+b \right)}^{3}}={{a}^{3}}+{{b}^{3}}+3ab\left( a+b \right)$ and ${{\left( a-b \right)}^{3}}={{a}^{3}}-{{b}^{3}}-3ab\left( a-b \right)$.