Question

Square of (0.98) ^2 using identity

Answer 1

Solution :

$\bf (0.98)^{2}$

Now, As we can write 0.98 = 1.00 - 0.02

$\bf : \implies (0.98)^{2} = (1.00 - 0.02)^{2}$

Now, by using identinty,

$\Large \boxed{ \pink{\bf (a - b)^{2} = a^{2} + b^{2} - 2ab}}$

$\bf : \implies (0.98)^{2} = (1.00)^{2} + (0.02)^{2} - 2 \times (1.00) \times (0.02)$

$\bf : \implies (0.98)^{2} = (1)^{2} + (\dfrac{2}{100})^{2} - 2 \times 1 \times \dfrac{2}{100}$

$\bf : \implies (0.98)^{2} = 1 + \dfrac{4}{10000} - 2 \times \dfrac{2}{100}$

$\bf : \implies (0.98)^{2} = \dfrac{10000 + 4}{10000} - \dfrac{4}{100}$

$\bf : \implies (0.98)^{2} = \dfrac{10004}{10000} - \dfrac{4}{100}$

$\bf : \implies (0.98)^{2} = \dfrac{10004}{10000} - \dfrac{400}{10000}$

$\bf : \implies (0.98)^{2} = \dfrac{10004 - 400}{10000}$

$\bf : \implies (0.98)^{2} = \dfrac{9604}{10000}$

$\bf : \implies (0.98)^{2} = 0.9604$

Therefore, answer is 0.9604.

Answer 2

We can also write,

(0.98)² = (1 - 0.02)²

Now we know,

(a - b)² = a² - 2ab + b²

Arranging,

(1 - 0.02)² = 1² - 2(1)(0.02) + (0.02)²

= 1 - 0.04 + 0.0004

= 0.9604

{Answer}