Question

quando possivel, simplifique os numeros irracionais que estao nos radicais a seguir. .a)$\sqrt[3]{250}$= .b)$\sqrt{1875}$= .c)$\sqrt[5]{192}$= .d)7$\sqrt[3]{250}$= .e)$\sqrt[6]{7^{2} X 2^{3} }$= .f)$\sqrt[15]{11^{6} X 2^{9} }$= .g)$\sqrt[6]{320}$= .h)$\sqrt[4]{1296}$=

Answer 1

Oie, Td Bom?!

a)

$\sqrt[3]{250}$

$\sqrt[3]{5 {}^{3} \times 2}$

$\sqrt[3]{5 {}^{3} } \sqrt[3]{2}$

$5 \sqrt[3]{2}$

b)

$\sqrt{1875}$

$\sqrt{25 {}^{2} \times 3}$

$\sqrt{25 {}^{2} } \sqrt{3}$

$25 \sqrt{3}$

c)

$\sqrt[5]{192}$

$\sqrt[5]{2 {}^{5} \times 6 }$

$\sqrt[5]{2 {}^{5} } \sqrt[5]{6}$

$2 \sqrt[5]{6}$

d)

$7\sqrt[3]{250}$

$7 \sqrt[3]{5 {}^{3} \times 2 }$

$7 \sqrt[3]{5 {}^{3} } \sqrt[3]{2}$

$7 \times 5 \sqrt[3]{2}$

$35 \sqrt[5]{2}$

e)

$\sqrt[6]{7 {}^{2} \times 2 {}^{3} }$

$\sqrt[6]{49 \times 8}$

$\sqrt[6]{392}$

f)

$\sqrt[15]{11 {}^{6} \times 2 {}^{9} }$

$\sqrt[15]{2 {}^{3} \times 22 {}^{6} }$

$\sqrt[15]{8 \times 113379904}$

$\sqrt[15]{907039232}$

g)

$\sqrt[6]{320}$

$\sqrt[6]{2 {}^{6} \times 5}$

$\sqrt[6]{2 {}^{6} } \sqrt[6]{5}$

$2 \sqrt[6]{5}$

h)

$\sqrt[4]{1296}$

$\sqrt[4]{6 {}^{4} }$

$6$

Att. Makaveli1996

Answer 2

Explicação passo-a-passo:

a)

$\sf \sqrt[3]{250}$

$\sf =\sqrt[3]{2\cdot5^3}$

$\sf =\red{5\sqrt[3]{2}}$

b)

$\sf \sqrt{1875}$

$\sf =\sqrt{3\cdot5^4}$

$\sf =\sqrt{3\cdot(5^2)^2}$

$\sf =5^2\sqrt{3}$

$\sf =\red{25\sqrt{3}}$

c)

$\sf \sqrt[5]{192}$

$\sf =\sqrt[5]{2^6\cdot3}$

$\sf =\sqrt[5]{2^5\cdot2\cdot3}$

$\sf =2\sqrt[5]{2\cdot3}$

$\sf =\red{2\sqrt[5]{6}}$

d)

$\sf 7\sqrt[3]{250}$

$\sf =7\sqrt[3]{2\cdot5^3}$

$\sf =7\cdot5\sqrt[3]{2}$

$\sf =\red{35\sqrt[3]{2}}$

e)

$\sf \sqrt[6]{7^2\cdot2^3}$

$\sf =\sqrt[6]{7^2}\cdot\sqrt[6]{2^3}$

$\sf =\sqrt[6\div2]{7^{2\div2}}\cdot\sqrt[6\div3]{2^{3\div3}}$

$\sf =\red{\sqrt[3]{7}\cdot\sqrt[2]{2}}$

f)

$\sf \sqrt[15]{11^6\cdot2^9}$

$\sf =\sqrt[15]{11^6}\cdot\sqrt[15]{2^9}$

$\sf =\sqrt[15\div3]{11^{6\div3}}\cdot\sqrt[15\div3]{2^{9\div3}}$

$\sf =\sqrt[5]{11^2}\cdot\sqrt[5]{2^3}$

$\sf =\sqrt[5]{121}\cdot\sqrt[5]{8}$

$\sf =\red{\sqrt[5]{968}}$

g)

$\sf \sqrt[6]{320}$

$\sf =\sqrt[6]{2^6\cdot5}$

$\sf =\red{2\sqrt[6]{5}}$

h)

$\sf \sqrt[4]{1296}$

$\sf =\sqrt[4]{2^4\cdot3^4}$

$\sf =2\cdot3$

$\sf =\red{6}$