Question

1. Answer the following question:
(1) By using formula find the value of 99²
​

Answer 1

1 =99²

= (100 -1)2

= 1002 - 200 + 12

= 10000 - 200 + 1

= 9801

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Answer 2

Working out:

Here, we are asked to find the value of 99² by using a formula or an Identity. It means, we don't have to multiply it directly rather solving by using a shortcut method.

So, Given

➝ 99²

It can be written as,

➝ (100 - 1)²

Now look at this form of the square number. If we consider a = 100 and b = 1, then it will be (a - b)². So, let's use this identity,

• (a - b)² = a² - 2ab + b²

Plug the values of a and b, we had considered before:

➝ (100 - 1)²

By using the formula,

➝ 100² - 2(100)(1) + 1²

➝ 10000 - 200 + 1

➝ 10000 + 1 - 200

➝ 10001 - 200

➝ 9801

So, the value of 99²:

$\large{ \boxed{ \red{ \bf{9801}}}}$

And we are done !!

Tip:

Here, I have used this method with all the steps, but during fast and objective questions, try doing it mentally or in 1-2 steps for saving time.

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