Question

Find the squares of 99 using the identity ${(a-b)}^2=a^2-2ab+b^2$ ?

Answer 1

Hint: We need to find the square of the number 99. Firstly, we write the given number 99 as the difference between 100 and 1. Then, we use the formula of ${(a-b)}^2$ in mathematics to get the square of the number 99.

Complete step by step solution:
We are given a number and need to find out the value of ${99}^2$ . We will be solving the given question by writing the number 99 as the difference between 100 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 find the square of a given number 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,
$\therefore 5^2=25$
According to our question, we need to find the value of ${99}^2$ using an identity.
Expressing the number 99 as the difference between 100 and 1, we get,
$\Rightarrow 99=(100-1)$
Squaring the above equation on both sides, we get,
$\Rightarrow {99}^2={(100-1)}^2$
The formula of ${(a-b)}^2$ is given by
$\Rightarrow {(a-b)}^2=a^2+b^2-2ab$
Here,
a: 100
b: 1
Applying the same for the above equation, we get,
$\Rightarrow {99}^2={100}^2+1^2-(2\times 100\times 1)$
Simplifying the above equation, we get,
$\Rightarrow {99}^2=10000+1-\left(200\right)$
Let us evaluate it further.
$\Rightarrow {99}^2=10000+(1-200)$
$\Rightarrow {99}^2=10000-199$
$\therefore {99}^2=9801$

The value of the square of the number 99 is 9801.

Note: The result can be cross-checked by applying the square root on both sides of the equation ${99}^2=9801$ .
LHS:
$\Rightarrow \sqrt{{\left(99\right)}^2}$
$\Rightarrow 99$
RHS:
$\Rightarrow \sqrt{9801}$
$\Rightarrow \sqrt{{\left(99\right)}^2}$
$\Rightarrow 99$
LHS = RHS. The result attained is correct.