9.7 Higher roots  (Page 4/8)

ⓐ $\sqrt[3]{216}$
ⓑ $\sqrt[4]{256}$
ⓒ $\sqrt[5]{32}$

ⓐ $\sqrt[3]{27}$
ⓑ $\sqrt[4]{16}$
ⓒ $\sqrt[5]{243}$

ⓐ $\sqrt[3]{512}$
ⓑ $\sqrt[4]{81}$
ⓒ $\sqrt[5]{1}$

ⓐ $\sqrt[3]{125}$
ⓑ $\sqrt[4]{1296}$
ⓒ $\sqrt[5]{1024}$

ⓐ $\sqrt[3]{\mathrm{-8}}$
ⓑ $\sqrt[4]{\mathrm{-81}}$
ⓒ $\sqrt[5]{\mathrm{-32}}$

ⓐ $\sqrt[3]{\mathrm{-64}}$
ⓑ $\sqrt[4]{\mathrm{-16}}$
ⓒ $\sqrt[5]{\mathrm{-243}}$

ⓐ $\sqrt[3]{\mathrm{-125}}$
ⓑ $\sqrt[4]{\mathrm{-1296}}$
ⓒ $\sqrt[5]{\mathrm{-1024}}$

ⓐ $\sqrt[3]{\mathrm{-512}}$
ⓑ $\sqrt[4]{\mathrm{-81}}$
ⓒ $\sqrt[5]{\mathrm{-1}}$

ⓐ $\sqrt[5]{u^5}$
ⓑ $\sqrt[8]{v^8}$

ⓐ $\sqrt[3]{a^3}$
ⓑ

ⓐ $\sqrt[4]{y^4}$
ⓑ $\sqrt[7]{m^7}$

ⓐ $\sqrt[8]{k^8}$
ⓑ $\sqrt[6]{p^6}$

ⓐ $\sqrt[3]{x^9}$
ⓑ $\sqrt[4]{y^{12}}$

ⓐ $\sqrt[5]{a^{10}}$
ⓑ $\sqrt[3]{b^{27}}$

ⓐ $\sqrt[4]{m^8}$
ⓑ $\sqrt[5]{n^{20}}$

ⓐ $\sqrt[6]{r^{12}}$
ⓑ $\sqrt[3]{s^{30}}$

ⓐ $\sqrt[4]{16x^8}$
ⓑ $\sqrt[6]{64y^{12}}$

ⓐ $\sqrt[3]{\mathrm{-8}{c}^9}$
ⓑ $\sqrt[3]{125d^{15}}$

ⓐ $\sqrt[3]{216a^6}$
ⓑ $\sqrt[5]{32b^{20}}$

ⓐ $\sqrt[7]{128r^{14}}$
ⓑ $\sqrt[4]{81s^{24}}$

ⓐ $\sqrt[3]{r^5}$ ⓑ $\sqrt[4]{s^{10}}$

ⓐ $\sqrt[5]{u^7}$ ⓑ $\sqrt[6]{v^{11}}$

ⓐ $\sqrt[4]{m^5}$ ⓑ $\sqrt[8]{n^{10}}$

ⓐ $\sqrt[5]{p^8}$ ⓑ $\sqrt[3]{q^8}$

ⓐ $\sqrt[4]{32}$ ⓑ $\sqrt[5]{64}$

ⓐ $\sqrt[3]{625}$ ⓑ $\sqrt[6]{128}$

ⓐ $\sqrt[5]{64}$ ⓑ $\sqrt[3]{256}$

ⓐ $\sqrt[4]{3125}$ ⓑ $\sqrt[3]{81}$

ⓐ $\sqrt[3]{108x^5}$ ⓑ $\sqrt[4]{48y^6}$

ⓐ $\sqrt[5]{96a^7}$ ⓑ $\sqrt[3]{375b^4}$

ⓐ $\sqrt[4]{405m^{10}}$ ⓑ $\sqrt[5]{160n^8}$

ⓐ $\sqrt[3]{512p^5}$ ⓑ $\sqrt[4]{324q^7}$

ⓐ $\sqrt[3]{\mathrm{-864}}$ ⓑ $\sqrt[4]{\mathrm{-256}}$

ⓐ $\sqrt[5]{\mathrm{-486}}$ ⓑ $\sqrt[6]{\mathrm{-64}}$

ⓐ $\sqrt[5]{\mathrm{-32}}$ ⓑ $\sqrt[8]{\mathrm{-1}}$

ⓐ $\sqrt[3]{\mathrm{-8}}$ ⓑ $\sqrt[4]{\mathrm{-16}}$

ⓐ $\sqrt[3]{\frac{p^{11}}{p^2}}$ ⓑ $\sqrt[4]{\frac{q^{17}}{q^{13}}}$

ⓐ $\sqrt[5]{\frac{d^{12}}{d^7}}$ ⓑ $\sqrt[8]{\frac{m^{12}}{m^4}}$

ⓐ $\sqrt[5]{\frac{u^{21}}{u^{11}}}$ ⓑ $\sqrt[6]{\frac{v^{30}}{v^{12}}}$

ⓐ $\sqrt[3]{\frac{r^{14}}{r^5}}$ ⓑ $\sqrt[4]{\frac{c^{21}}{c^9}}$

ⓐ $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$ ⓑ $\frac{\sqrt[5]{128x^8}}{\sqrt[5]{2x^2}}$

ⓐ $\frac{\sqrt[3]{\mathrm{-625}}}{\sqrt[3]{5}}$ ⓑ $\frac{\sqrt[4]{80m^7}}{\sqrt[4]{5m}}$

ⓐ $\sqrt[3]{\frac{1050}{2}}$ ⓑ $\sqrt[4]{\frac{486y^9}{2y^3}}$

ⓐ $\sqrt[3]{\frac{162}{6}}$ ⓑ $\sqrt[4]{\frac{160r^{10}}{5r^3}}$

ⓐ $\sqrt[3]{\frac{54a^8}{b^3}}$ ⓑ $\sqrt[4]{\frac{64c^5}{d^2}}$

ⓐ $\sqrt[5]{\frac{96r^{11}}{s^3}}$ ⓑ $\sqrt[6]{\frac{128u^7}{v^3}}$

ⓐ $\sqrt[3]{\frac{81s^8}{t^3}}$ ⓑ $\sqrt[4]{\frac{64p^{15}}{q^{12}}}$

ⓐ $\sqrt[3]{\frac{625u^{10}}{v^3}}$ ⓑ $\sqrt[4]{\frac{729c^{21}}{d^8}}$

ⓐ $\sqrt[7]{8p}+\sqrt[7]{8p}$
ⓑ $3\sqrt[3]{25}-\sqrt[3]{25}$

ⓐ $\sqrt[3]{15q}+\sqrt[3]{15q}$
ⓑ $2\sqrt[4]{27}-6\sqrt[4]{27}$

ⓐ $3\sqrt[5]{9x}+7\sqrt[5]{9x}$
ⓑ $8\sqrt[7]{3q}-2\sqrt[7]{3q}$

ⓐ
ⓑ

ⓐ $\sqrt[3]{81}-\sqrt[3]{192}$
ⓑ $\sqrt[4]{512}-\sqrt[4]{32}$

ⓐ $\sqrt[3]{250}-\sqrt[3]{54}$
ⓑ $\sqrt[4]{243}-\sqrt[4]{1875}$

ⓐ $\sqrt[3]{128}+\sqrt[3]{250}$
ⓑ $\sqrt[5]{729}+\sqrt[5]{96}$

ⓐ $\sqrt[4]{243}+\sqrt[4]{1250}$
ⓑ $\sqrt[3]{2000}+\sqrt[3]{54}$

ⓐ $\sqrt[3]{64a^{10}}-\sqrt[3]{\mathrm{-216}{a}^{12}}$
ⓑ $\sqrt[4]{486u^7}+\sqrt[4]{768u^3}$

ⓐ $\sqrt[3]{80b^5}-\sqrt[3]{\mathrm{-270}{b}^3}$
ⓑ $\sqrt[4]{160v^{10}}-\sqrt[4]{1280v^3}$

$\sqrt[4]{16}$

$\sqrt[6]{64}$

$\sqrt[3]{a^3}$

$\sqrt[3]{\mathrm{-8}{c}^9}$

$\sqrt[3]{125d^{15}}$

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

$\sqrt[4]{s^{10}}$

$\sqrt[3]{108x^5}$

$\sqrt[4]{48y^6}$

$\sqrt[5]{\mathrm{-486}}$

$\sqrt[6]{\mathrm{-64}}$

$\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$

$\frac{\sqrt[5]{128x^8}}{\sqrt[5]{2x^2}}$

$\sqrt[5]{\frac{96r^{11}}{s^3}}$

$\sqrt[6]{\frac{128u^7}{v^3}}$

$\sqrt[3]{81}-\sqrt[3]{192}$

$\sqrt[4]{512}-\sqrt[4]{32}$

$\sqrt[3]{64a^{10}}-\sqrt[3]{\mathrm{-216}{a}^{12}}$

$\sqrt[4]{486u^7}+\sqrt[4]{768u^3}$

Population growth The expression $10·x^n$ models the growth of a mold population after $n$ generations. There were 10 spores at the start, and each had $x$ offspring. So $10·x^n$ is the number of offspring at the fifth generation. At the fifth generation there were 10,240 offspring. Simplify the expression $\sqrt[5]{\frac{\mathrm{10,240}}{10}}$ to determine the number of offspring of each spore.

Spread of a virus The expression $3·x^n$ models the spread of a virus after $n$ cycles. There were three people originally infected with the virus, and each of them infected $x$ people. So $3·x^4$ is the number of people infected on the fourth cycle. At the fourth cycle 1875 people were infected. Simplify the expression $\sqrt[4]{\frac{1875}{3}}$ to determine the number of people each person infected.

Explain how you know that $\sqrt[5]{x^{10}}=x^2$ .

Explain why $\sqrt[4]{\mathrm{-64}}$ is not a real number but $\sqrt[3]{\mathrm{-64}}$ is.