Question

the value of (99.8)^1/2 according to binomial approximation​

Answer 1

we have to find value of (99.8)½ according to Binomial approximation.

We know, according to Binomial theorem,

if Any number in the form of (1 ± a)ⁿ , where a << 1

Then, (1 ± a)ⁿ ≈ 1 ± na

Now, (99.8)⅓ = (100 - 0.2)½

= (100)½ [1 - 0.2/100]½

= (10²)½ [ 1 - 0.002]½

= (10) [1 - 0.002]½

obviously, 1 >> 0.002

so, (1 - 0.002)½ ≈ 1 - 1/2 × 0.002

= 1 - 0.001

= 0.999

now, (10) [1 - 0.002]½ = 10 × 0.999 = 9.99

hence, (99.8)½ ≈ 9.99

Answer 2

$\huge\bold\purple{Answer:-}$

we have to find value of (99.8)½ according to Binomial approximation.

We know, according to Binomial theorem,

if Any number in the form of (1 ± a)ⁿ , where a << 1

Then, (1 ± a)ⁿ ≈ 1 ± na

Now, (99.8)⅓ = (100 - 0.2)½

= (100)½ [1 - 0.2/100]½

= (10²)½ [ 1 - 0.002]½

= (10) [1 - 0.002]½

obviously, 1 >> 0.002

so, (1 - 0.002)½ ≈ 1 - 1/2 × 0.002

= 1 - 0.001

= 0.999

now, (10) [1 - 0.002]½ = 10 × 0.999 = 9.99

hence, (99.8)½ ≈ 9.99