упростить выражения:

Question 1

Question 2

Решите задачу:

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

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

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

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

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

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

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

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

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