Question

What is 39 squared?

Answer 1

Hint: We need to find the square of the number 39. Firstly, we write the given number 39 as the difference between 40 and 1. Then, we use the formula of ${(a-b)}^2$ in mathematics to get the square of the number 39.

Complete step by step answer:
We are given a number and need to find out the value of ${39}^2$ . We will be solving the given question by writing the number 39 as the difference between 40 and 1 and then evaluating the expression using the formula of ${(a-b)}^2$ .
The square of a number is defined as the result of multiplying the number by itself. The square of a number $n$ is given by $n\times n$ also written as $n^2$ .
Let us now understand how to solve the given question through an example.
Example:
What is 5 squared?
The square of the number 5 is obtained by multiplying the number 5 with itself.
Applying the same, we get,
$\Rightarrow 5\times 5$
The product of number with itself that is $n\times n$ can be also written as $n^2$ .
Writing the same, we get,
$\Rightarrow 5^2$
The result of the above expression is $25$
Substituting the same, we get,
$\therefore 5^2=25$
Now,
$\Rightarrow 39=(40-1)$
Squaring the above equation on both sides, we get,
$\Rightarrow {39}^2={(40-1)}^2$
The formula of ${(a-b)}^2$ is given by
$\Rightarrow {(a-b)}^2=a^2+b^2-2ab$
Here,
a: 40
b: 1
Applying the same for the above equation, we get,
$\Rightarrow {39}^2={40}^2+1^2-(2\times 40\times 1)$
Simplifying the above equation, we get,
$\Rightarrow {39}^2=1600+1-\left(80\right)$
Let us evaluate it further.
$\Rightarrow {39}^2=1600+(1-80)$
$\Rightarrow {39}^2=1600-79$
$\therefore {39}^2=1521$

The value of the number 39 is 1521.

Note: The square of a number that is a multiple of 10 can be easily found out as follows,
$\Rightarrow {40}^2={(10\times 4)}^2$
$\Rightarrow {40}^2={\left(10\right)}^2\times {\left(4\right)}^2$
$\Rightarrow {40}^2=100\times 16$
$\Rightarrow {40}^2=1600$
The result can be cross-checked by applying the square root on both sides of the equation ${39}^2=1521$ .
LHS:
$\Rightarrow \sqrt{{\left(39\right)}^2}$
$\Rightarrow 39$
RHS:
$\Rightarrow \sqrt{1521}$
$\Rightarrow \sqrt{{\left(39\right)}^2}$
$\Rightarrow 39$
LHS = RHS. The result attained is correct.