Question

16. Find the square of 99 without actual multiplication.​

Answer 1

Given number:- $99$

We have to find the square,

Square of the number $99$ ,

$=>99\times99=(99)^2$

It was also written as,

$=>(99)^2=(100-1)^{2}$

We have the formula of,

$(a-b)^2=a^2+b^2-2ab$

From, $(100-1)^2$ we have

$a=100,b=1$

By putting the above values in the formula

$(100-1)^2=(100)^2+(1)^2-2(100)(1)$

$=>10000+1-200$

$=>10001-200$

$=>9801$

Hence the square of $99$ is $9801$.

Answer 2

Given,

$99$

Find the square of $99$ without actual multiplication by using $(x-y)^{2}$ formula,

$(x-y)^{2}=x^{2}+y^{2}-2xy$

First we convert $99$ in the form of $(x-y)$

$99=(100-1)$

Squaring on both side

$99^{2}=(100-1)^{2}$

Here,

$x=100$, $y=1$

$99^{2}= 100^{2}+1^{2}-2\times1\times100$

$99^{2}=10000+1-200$

$99^{2}=9800$

$99^{2}=9801$

Therefore, $9801$ is the square of $99$.