Question

Considere que a e b são números reais positivos. Nessas condições, simplifique as radicais: A) Raiz quadrada de 9a elevado a 3 B) ab raiz cubica de 270 elevado a 4 C) ab raiz quadrada de a elevado a 2 e b elevado a 5

Answer 1

Explicação passo-a-passo:

a)

$\sf \sqrt{9a^3}$

$\sf =\sqrt{9a^2\cdot a}$

$\sf =\sqrt{(3a)^2\cdot a}$

$\sf =3a\sqrt{a}$

b)

$\sf ab\sqrt[3]{270^4}$

$\sf =ab\sqrt[3]{270^3\cdot270}$

$\sf =270ab\sqrt[3]{270}$

$\sf =270ab\sqrt[3]{3^3\cdot10}$

$\sf =3\cdot270ab\sqrt[3]{10}$

$\sf =810ab\sqrt[3]{10}$

c)

$\sf ab\sqrt{a^2b^5}$

$\sf =ab\sqrt{a^2b^4\cdot b}$

$\sf =ab\sqrt{(ab^2)^2\cdot b}$

$\sf =ab^2\cdot ab\sqrt{b}$

$\sf =a^2b^3\sqrt{b}$

Answer 2

Oie, Td Bom?!

A)

$= \sqrt{9a {}^{3} }$

$= \sqrt{3 {}^{2}a {}^{2} \: . \: a}$

$= \sqrt{3 {}^{2} } \sqrt{a {}^{2} } \sqrt{a}$

$= 3a \sqrt{a}$

B)

$= ab \sqrt[3]{270 {}^{4} }$

$= ab \sqrt[3]{270 {}^{3} \: . \: 270}$

$= ab \sqrt[3]{27 0{}^{3} } \sqrt[3]{270}$

$= ab \: . \: 270 \sqrt[3]{270}$

$= ab \: . \: 270 \sqrt[3]{3 {}^{3} \: . \: 10}$

$= ab \: . \: 270 \sqrt[3]{3 {}^{3} } \sqrt[3]{10}$

$= ab \: . \: 270 \: . \: 3 \sqrt[3]{10}$

$= 810 \sqrt[3]{10} ab$

C)

$= ab \sqrt{a {}^{2}b {}^{5} }$

$= ab \sqrt{a {}^{2} b {}^{4} \: . \: b}$

$= ab \sqrt{a {}^{2} } \sqrt{b {}^{4} } \sqrt{b}$

$= abab {}^{2} \sqrt{b}$

$= a {}^{2} b {}^{3} \sqrt{b}$

Att. Makaveli1996