Question

упростить выражения:

Answer 1

$2) sqrt[4]{2m^9}* sqrt[4]{8m^3}= sqrt[4]{2*8*m^{9+3}} = sqrt[4]{2^4*m^{12}}=2m^3$

$5) sqrt[3]{12-4 sqrt{5} }* sqrt[3]{12+4 sqrt{5} }= sqrt[3]{(12-4 sqrt{5})(12+4 sqrt{5}) }= \ \ sqrt[3]{12^2-(4 sqrt{5})^2 }=sqrt[3]{144-16*5 }=sqrt[3]{64 }=4$

$6) frac{ sqrt[3]{429}*9^ {frac{1}{3}} }{ sqrt[3]{143}} = sqrt[3]{ frac{429*9}{143} } =sqrt[3]{ frac{429*9}{143} }= sqrt[3]{3*9}=3$

$8) frac{ sqrt{12}* sqrt[3]{56} }{ sqrt{84 }}= sqrt{ frac{12}{84} }* sqrt[3]{8*7} = frac{sqrt[3]{8*7} }{ sqrt{7} }=2*7^{ frac{1}{3}- frac{1}{2}}=2*7^{- frac{1}{6}}= frac{ 2 }{ sqrt[6]{7} }$

$9) frac{ sqrt{75}* sqrt[3]{8} }{ sqrt{27} } =frac{ sqrt{3*25}* sqrt[3]{2^3} }{ sqrt{3*3^2} }=frac{5*2* sqrt{3} }{3* sqrt{3} }= frac{10}{3}=3 frac{1}{3}$

$13) frac{ sqrt[5]{y^{18}} }{ sqrt[5]{y^3}} = sqrt[5]{y^{18-3}} =sqrt[5]{y^{15}} =y^{15:5}=y^3$

$18) frac{ sqrt[3]{2}* sqrt{236} }{ sqrt{59} } = frac{ sqrt[3]{2}* sqrt{4*59} }{ sqrt{59} }=sqrt[3]{2}* sqrt{4}=2sqrt[3]{2}$

$22) frac{ sqrt{7} * sqrt[3]{49} }{ sqrt[6]{7} } =7^{ frac{1}{2}}* 7^{ frac{2}{3}}:7^{ frac{1}{6}}=7^{ frac{1}{2}+ frac{2}{3}- frac{1}{6}}=7^{ frac{6}{6}}=7$

$24) frac{ sqrt[4]{y^{15}} }{ sqrt[4]{y^5} } = sqrt[4]{y^{15-5}}= sqrt[4]{y^{10}}= sqrt[4]{y^{8}*y^2}=y^2* sqrt{y}$