Question

question 3 find the value of root under 3.1428 and root under 0.31428 correct to three decimal places.

Answer 1

Answer:

Step-by-step explanation:

√3.1428

1.7727

3.1428

1 1

2.1428

2.7 1.89

0.2528

3.47 0.2429

0.0099

3.542 0.007084

0.002816

3.5447 0.00248129

0.00033471

√3.1428 = 1.7727 = 1.773

√0.31428 = √314280/1000000 = (√314280)/1000

√314280 = 560.6

560.6

314280

5 2803

64280

106 636

680

1120 0

680.0

1120.6 672.36

7.64

√0.31428  = 560.6/1000 = 0.5606 = 0.561

Answer 2

Answer:

$\sqrt{3.1428}$≅ $1.7851$

Step-by-step explanation:

I have applied errors and approximation method to find square root of the given number.

$\sqrt{3.1428}$

Let $y=f(x)=\sqrt{x}=x^{\frac{1}{2}}$

Take, x=4 and Δx=dx=-0.8572

$dy=\frac{1}{2\sqrt{x}}\:dx$

$dy=\frac{1}{2\sqrt{4}}\:(-0.8572)$

$dy=\frac{1}{2(2)}\:(-0.8572)$

$dy=\frac{1}{4}\:(-0.8572)$

$dy=-0.2143$

Now

$\sqrt{3.1428}$

$=f(3.1428)$

$=f(4-0.8572)$

$=f(4+(-0.8572))$

$=f(4+\Delta{x})$

≅$f(4)+dy$

≅$\sqrt{4}+(-0.2143)$

≅$2+(-0.2143)$

≅$1.7851$

$\sqrt{3.1428}$≅$1.7851$