Question

Номер 1 (b,d) 2(a,c) 3(весь) 4(весь)

Answer 1

$\displaystyle 1).. \\ b)..( \sqrt[4]{8}- \sqrt[4]{0,5})* \sqrt[4]{2}= \sqrt[4]{8*2}- \sqrt[4]{0,5*2}=2-1=1 \\ \\ d).. \sqrt[3]{10+6 \sqrt{3}}* \sqrt[3]{10-6 \sqrt{3}}= \sqrt[3]{100-36*3}= \sqrt[3]{-8}=-2 \\ \\ 2).. \\ a).. \\ \sqrt[5]{3}=3^{1/5}=3^{3/15}=27^{1/15} \\ \sqrt[3]{2}=2^{1/3}=2^{5/15}=32^{1/15} \\ \sqrt[15]{30}=30^{1/15} \\ \\ 27^{1/15}\ \textless \ 30^{1/15}\ \textless \ 32^{1/15} \\ \sqrt[5]{3}\ \textless \ \sqrt[15]{30}\ \textless \ \sqrt[3]{2}$

$\displaystyle c).. \\ ( \frac{1}{2})^{1/2}=( \frac{1}{2})^{3/6}=( \frac{1}{8})^{1/6} \\ \\ ( \frac{1}{3})^{1/3}=( \frac{1}{3})^{2/6}=( \frac{1}{9})^{1/6} \\ \\ ( \frac{1}{4})^{1/2}=( \frac{1}{4})^{3/6}=( \frac{1}{64})^{1/6} \\ \\ ( \frac{1}{64})^{1/6}\ \textless \ ( \frac{1}{9})^{1/6}\ \textless \ ( \frac{1}{8})^{1/6} \\ \\ (\frac{1}{4})^{1/2}\ \textless \ (\frac{1}{3})^{1/3}\ \textless \ ( \frac{1}{2})^{1/2} \\ \\ 3).. \\ a).. \frac{12}{ \sqrt[3]{3}}= \frac{12 \sqrt[3]{9}}{ \sqrt[3]{27}}= \frac{12 \sqrt[3]{9}}{3}=4 \sqrt[3]{9}$

$\displaystyle b)..\frac{6}{ \sqrt[5]{8}}= \frac{6* \sqrt[5]{2^{2}}}{ \sqrt[5]{2^{3}*2^{2}}}= \frac{6* \sqrt[5]{4}}{2}=3 \sqrt[5]{4} \\ \\ c).. \frac{6}{ \sqrt[4]{32}+ \sqrt[4]{2}}= \frac{6}{2 \sqrt[4]{2}+ \sqrt[4]{2}}= \frac{2}{ \sqrt[4]{2}}= \frac{2* \sqrt[4]{2^{3}}}{ \sqrt[4]{2*2^{3}}}= \sqrt[4]{8}$

4).. V = 4/3 πR³
a).. V = 4/3 π(1,5)³ = 4*3,14*3,375/3 = 14,13 (м³)
b).. 28π/3 = 4/3 πR³
      R = ∛(28π/4π) = ∛7 ≈ 1,9 (м)