Question

the value of( 1.004)1/2 is​

Answer 1

To find: √1.004 = ?

Solution:

1.004 = 10040/10000

First we find square root of 10040 by long division method.

1 00 40 | 100.199

1 |

---------------

20 | 0

| 0

---------------

200 | 40

| 0

--------------

2001 | 4000

| 2001

----------------

20029 | 199900

| 180261

--------------------

200389 | 1963900

| 1803501

-----------------------

200398 | 160399

So √10040 = 100.199

Now, √1.004

= √(10040/10000)

= √10040 / √10000

= 100.199 / 100

= 1.00199 (approximately)

Answer 2

Given  : ( 1.004)1/2    , √1.004

To find : Approximate value

Solution:

f(x +  Δx)  = √1.004

x  = 1

Δx = 0.004

f(x) =  √x

f'(x) = 1/2√x

f(x +  Δx)  = f(x)  + f'(x) Δx

√1.004 = √1  + (1/2√1) (0.004)

=> √1.004 =  1  + (1/2) (0.004)

=> √1.004 =  1 + 0.002

=> √1.004 = 1.002

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