Question

The value of (4.008)^1/2 according to binomial expansion is

Answer 1

(4.008)^1/2

(4+0.008)^1/2

(4)^1/2 (1+0.008/4)^1/2

2 (1+(1/2*0.008/4))

2(1+0.001)

2*1.001

2.002

Answer 2

Answer: $[4(1+0.002)]^{\dfrac{1}{2}} =2.002$

Explanation:

$(4.008)^{\dfrac{1}{2}} = (4+0.008)^{\dfrac{1}{2}}$

Using binomial expansion

$(1+x)^{n} = 1+nx+\dfrac{n(n-1)}{2}x^{2}........$

$[4(1+0.002)]^{\dfrac{1}{2}} = 2[1+\dfrac{1}{2}\times(0.002)+\dfrac{\dfrac{1}{2}(\dfrac{1}{2}-1)}{2}\times(0.002)^{2}...]$

Neglected of higher terms

So,

$[4(1+0.002)]^{\dfrac{1}{2}} =2[1+0.001]$

$[4(1+0.002)]^{\dfrac{1}{2}} =2.002$

Hence, this is the required solution.