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 ${{\left( a-b \right)}^{2}}$ 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 ${{\left( a-b \right)}^{2}}$ .
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,
$\Rightarrow 39=\left( 40-1 \right)$
Squaring the above equation on both sides, we get,
$\Rightarrow {{39}^{2}}={{\left( 40-1 \right)}^{2}}$
The formula of ${{\left( a-b \right)}^{2}}$ is given by
$\Rightarrow {{\left( a-b \right)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab$
Here,
a: 40
b: 1
Applying the same for the above equation, we get,
$\Rightarrow {{39}^{2}}={{40}^{2}}+{{1}^{2}}-\left( 2\times 40\times 1 \right)$
Simplifying the above equation, we get,
$\Rightarrow {{39}^{2}}=1600+1-\left( 80 \right)$
Let us evaluate it further.
$\Rightarrow {{39}^{2}}=1600+\left( 1-80 \right)$
$\Rightarrow {{39}^{2}}=1600-79$
$\therefore {{39}^{2}}=1521$

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,
$\Rightarrow {{40}^{2}}={{\left( 10\times 4 \right)}^{2}}$
$\Rightarrow {{40}^{2}}={{\left( 10 \right)}^{2}}\times {{\left( 4 \right)}^{2}}$
$\Rightarrow {{40}^{2}}=100\times 16$
$\Rightarrow {{40}^{2}}=1600$
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.