Question

Calculate the approximate value of √26 by taylor expansion

Answer 1

hey mate...approx value of
$\sqrt{26} =5$
hope this helps you ☺☺

Answer 2

Given: √26

To find: Approx. value of an expression using Taylor Expansion

Solution:

Taylor Series is given by -

f (a + h) = f (a) + h. f'(a) + h²/2! . f'' (a) + h³/3! . f''' (a) + . . .

We can write 26 as (25 + 1)

Expressing this as a function,

f (26) = f (25 + 1)

Thus, a = 25 and h = 1

Hence,

f (a) = √a = √25 = 5

f' (a) = 1/2 a^(1/2 - 1) = 1 / (2 . a^(1/2) ) = 1 / (2 .25^(1/2) ) = 0.1

Similarly,

f'' (a) = -0.002

f''' (a) = 0.00012

From Taylor series method, we have

√26 = f (a+1) = 5 + 0.1 + (-0.002/2!) + (0.00012/3!)

       = 5.09902

Therefore,

√26 = 5.09902