Question

please answer the question ​

Answer 1

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

$(ii) \: (8. {9)}^{2} = {(9 - 0.1)}^{2} \\ {(9 - 0.1)}^{2} = {9}^{2} + {0.1}^{2} - 2 \times 9 \times 0.1 \\ = 81 + 0.01 - 1.8 \\ = 79.21$

Answer 2

GiveN:-

• (99)²
• (8.9)²

To FinD:-

Evaluation.

Solution :

Analysis :

Here we have to add and subtract to evaluate with their actual identities. Then by using the required formula we can find them out.

ExplanatioN :

1)) (99)² :

Here we can take that (90 + 9) which equals to 99. As 99 is in square so our required number will be (90 + 9)².

By using the identity of,

(a + b)² = a² + 2ab + b²

where,

• a = 90
• b = 9

Using the required formula and substituting the required values,

⇒(a + b)²

⇒(90 + 9)²

Splitting it in a² + 2ab + b²,

⇒90² + 2.90.9 + 9²

⇒8100 + 1620 + 81

⇒9801

∴ (99)² = 9801.

____________________

2)) (8.9)² :

Here we can take that (10.0 - 1.1) which equals to 8.9. As 8.9 is in square so our required number will be (10.0+ 1.1)².

By using the identity of,

(a - b)² = a² - 2ab + b²

where,

• a = 10.0
• b = 1.1

Using the required formula and substituting the required values,

⇒(a - b)²

⇒(10.0- 1.1)²

Splitting it in a² - 2ab + b²,

⇒10.0²- 2.10.0.1.1 + 1.1²

⇒100 - 22 + 1.21

⇒100 + 1.21 - 22

⇒101.21 - 22

⇒79.21

∴ (8.9)² = 79.21.

1)) (99)² = 9801.

2)) (8.9)² = 79.21.