Question

(399)¹/²,Find approximate value.

Answer 1

we have to find out approximate value of (399)^½
using binomial expansion , if y = (a + b)ⁿ is a expression in such a way that y = aⁿ (1 + b/a)ⁿ
where 1 >> b/a then, y ≈ aⁿ (1 + nb/a)

here, (399)^½

= (400 - 1)^½

= {400(1 - 1/400)}^½

= (400)½ (1 - 1/400)½

here it is clear that 1 >> 1/400
so, we can definitely apply binomial expansion.

= 20(1 - 1/2 × 1/400)

= 20(1 - 1/800)

= 20(1 - 0.01/8)

= 20(1 - 0.00125)

= 20(0.99875)

= 20 × 0.99875

= 19.9750

hence, approximate value of (399)^½ ≈ 19.9750

Answer 2

Dear Student:

For finding we will define x =400

and Δx=-1

and use,Δy=dy/dx*(Δx)

And,also Δy=f(x+Δx)-f(x)

See the attachment: