Question

justifique por que √4,84 = 2,2

Answer 1

Pois 2,2 vezes 2,2 é igual a √4,84.

Answer 2

Usaremos as seguintes propriedades:

$\bullet\,\,\,\sqrt[n]{a^{m}}=a^{m/n}\\\\\\\bullet\,\,\,a^{m}\cdot b^{m}=(a\cdot b)^{m}\\\\\\\bullet\,\,\,\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$
_____________________________

$\sqrt{4,84}=\sqrt\dfrac{484}{100}}\\\\\\\sqrt{4,84}=\dfrac{\sqrt{484}}{\sqrt{100}}\\\\\\\sqrt{4,84}=\dfrac{\sqrt{484}}{10}$

Agora, vamos fatorar o número 484:

484 | 2
242 | 2
121 | 11
011 | 11
001

Portanto:

$484=2\cdot2\cdot11\cdot11=2^{2}\cdot11^{2}=(2\cdot11)^{2}=22^{2}$

Então:

$\sqrt{4,84}=\dfrac{\sqrt{484}}{10}\\\\\\\sqrt{4,84}=\dfrac{\sqrt{22^{2}}}{10}\\\\\\\sqrt{4,84}=\dfrac{\sqrt[2]{22^{2}}}{10}\\\\\\\sqrt{4,84}=\dfrac{22^{2/2}}{10}\\\\\\\sqrt{4,84}=\dfrac{22^{1}}{10}\\\\\\\sqrt{4,84}=\dfrac{22}{10}\\\\\\\boxed{\boxed{\sqrt{4,84}=2,2}}$