Quickly Squaring 99

$(99)^2=(100-1)^2 \\ =10000+1-200 \\ =\boxed{9801}$

Note : $(a\; \pm \; b)^2 = a^2 \; \pm 2ab + b^2$ .

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

$\Rightarrow 99^2 = (98)(100) + 1 = \boxed{9801}$

99*100= 9900

9900-99=9801

Here's another pretty way to tackle this problem.

Let me get my point through with some examples.

Take $\large 25^2 = 625$ . Note that $\large 26^2 = 676 = 25^2 + (25+26)$ . Similarly, $\large 24^2 = 576 = 25^2 - (25+24)$ .

Some other illustrations of this fact can be seen in $\large 11^2 = 121 = 10^2 + (11+10)$ , $\large 9^2 = 81 = 10^2 - (10+9)$ .

Therefore $\large 99^2 = 9801= 100^2 - (100+199)$

$99^2 = 9^2 \cdot 11 \cdot 11=891\cdot11=9801$

(99)2 = 99-1 = 98 and join 01.It becomes 9801

There is a really useful method to deal with squared numbers close to 100.

• 1) Let's take 96 as an example.

• 2) 100 - 96 = 4

• 3) 96 - 4 = 92

• 4) 4^2 = 16

• 5) Then, we group the answer of 3) with 4) as follows: 97^2 = 9216

For the numbers near 100 like 90,91,92,93,94,95,96,97,98,99 99 99 96 98 94 97 100-99=1 100-96=4 100-94=6 100-99=1 100-98=2 100-97=3 1+1=2 4+2=6 6+3= 9 100-2=98 100-6=94 100-9=91 1 1=01 4 2=08 6 3=18
99 99= 9801 96 98= 9408 94*97=9118