The approximate value of √[5]33 correct to 4 decimal places is

Question

The approximate value of √[5]33 correct to 4 decimal places is (A) 2.0000 (B) 2.1001 (C) 2.0125 (D) 2.0500

Tardigrade Admin · Accepted Answer

Let f(x)=x1 / 5 =(32+1)1 / 5 Here, a=32, h=(1/5), ∴ f(a+b) =f(a)+h f prime(a) ∴ (32+1)1 / 5 =(32)1 / 5+(1/5) × (1/(32)4 / 5) =2+(1/80)=2+0.0125 =2.0125

Q. The approximate value of $533$ correct to $4$ decimal places is

$2.0000$

$2.1001$

$2.0125$

$2.0500$

Let $f (x) = x^{1/5}$
$= (32 + 1)^{1/5}$
Here, $a = 32, h = \frac{1}{5},$
$∴ f (a + b) = f (a) + h f^{'} (a)$
$∴ (32 + 1)^{1/5} = (32)^{1/5} + \frac{1}{5} \times \frac{1}{( 32 ) ^{4/5}}$
$= 2 + \frac{1}{80} = 2 + 0.0125$
$= 2.0125$

Q. The approximate value of 533​ correct to 4 decimal places is

2.0000

2.1001

2.0125

2.0500