Question

Encontre a raíz quadrada aproximada de :
A) 51
B) 572
C) 5
D) 7
obs: preciso do cálculo

Answer 1

Vejamos :

A)

$\sqrt{N}\approx\dfrac{N + B}{2\sqrt{B}}$
$\sqrt{51}\approx\dfrac{51 + 49}{2\sqrt{49}}$
$\sqrt{51}\approx\dfrac{100}{2\sqrt{49}}$
$\sqrt{51}\approx\dfrac{100}{2.7}}$
$\sqrt{51}\approx\dfrac{100}{14}}$
$\sqrt{51}\approx\ 7,14$


$\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\sqrt{51}\approx\ 7,14}}}}}}}}}$



B)
$\sqrt{N}\approx{N + B}{2\sqrt{B}}$
$\sqrt{572}\approx\dfrac{572 + 523}{2\sqrt{529}}$
$\sqrt{572}\approx\dfrac{1101}{2\sqrt{529}}$
$\sqrt{572}\approx\dfrac{1101}{2.23}}$
$\sqrt{572}\approx\dfrac{1101}{46}}$
$\sqrt{572}\approx\ 23,9$



$\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\sqrt{7}\approx\ 23,9}}}}}}}}}$

C)
$\sqrt{N}\approx\dfrac{N + B}{2\sqrt{N}}$
$\sqrt{5}\approx\dfrac{5 + 4}{2\sqrt{4}}$
$\sqrt{5}\approx\dfrac{9}{2\sqrt{4}}$
$\sqrt{5}\approx\dfrac{9}{2.2}}$
$\sqrt{5}\approx\dfrac{9}{4}}$
$\sqrt{5}\approx\ 2,2$



$\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\sqrt{5}\approx\ 2,2}}}}}}}}}$

D
$\sqrt{7}\approx\dfrac{N + B}{2\sqrt{B}}$
$\sqrt{7}\approx\dfrac{7 + 4}{2\sqrt{4}}$
$\sqrt{7}\approx\dfrac{11}{2\sqrt{4}}$
$\sqrt{7}\approx\dfrac{11}{2.2}}$
$\sqrt{7}\approx\dfrac{11}{4}}$
$\sqrt{7}\approx\ 2,7$



$\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\sqrt{7}\approx\ 2,7}}}}}}}}}$



$\checkmark{\checkmark{\checkmark{\checkmark{\checkmark{\checkmark}}}}}}$

Mas também existe uma sequência infinita que eu mesmo inventei que dar a resposta :

A)

7 X 7 = 49
71 X 71 = 5041
714 X 714 = 509796
7141 X 7141 = 50993881

A fórmula consiste em atuar nos termos ou seja a resposta é :

√51 ≈ 7,141

B)

23 X 23 = 529
239 X 239 = 57121
2391 X 2391 = 5716881
23916 X 23916 = 571975056

√572 ≈ 23,916

C)

2 X 2 = 4
22 X 22 = 484
223 X 223 = 49729
2236 X 2236 = 4999696

√5 ≈ 2,236

D)

2 X 2 = 4
26 X 26 = 676
264 X 264 = 69696
2645 X 2645 = 6996025

√7 ≈ 2,645

★★★★★★★★★