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1
![sqrt[4]{(-7)^4} =7 sqrt[4]{(-7)^4} =7](https://tex.z-dn.net/?f=+sqrt%5B4%5D%7B%28-7%29%5E4%7D+%3D7)
∛(9*375)=∛3(27*125)=3*5=15
2
![sqrt[5]{7} = sqrt[10]{49} sqrt[5]{7} = sqrt[10]{49}](https://tex.z-dn.net/?f=+sqrt%5B5%5D%7B7%7D+%3D+sqrt%5B10%5D%7B49%7D+)
![sqrt[5]{7} textgreater sqrt[10]{47} sqrt[5]{7} textgreater sqrt[10]{47}](https://tex.z-dn.net/?f=+sqrt%5B5%5D%7B7%7D++textgreater+++sqrt%5B10%5D%7B47%7D+)
3
x³-125=0
x³=125
x=5
![sqrt[6]{x} =a sqrt[6]{x} =a](https://tex.z-dn.net/?f=+sqrt%5B6%5D%7Bx%7D+%3Da)
a²-3a-4=0
a1+a2=3 U a1*a2=-4
a1=-1⇒
нет решения
a2=4⇒
⇒x=4096
4
∛(12+4√5)*∛(12-4√5)=∛[(12+4√5)(12-4√5)]=∛(144-80)=∛64=4
![sqrt[4]{a^4} + sqrt[3]{a^3} =-a+a=0,a textless 0 sqrt[4]{a^4} + sqrt[3]{a^3} =-a+a=0,a textless 0](https://tex.z-dn.net/?f=+sqrt%5B4%5D%7Ba%5E4%7D+%2B+sqrt%5B3%5D%7Ba%5E3%7D+%3D-a%2Ba%3D0%2Ca+textless++0)
5
(3-√3)/(3+√3)=(3-√3)²/(3-√3)(3+√3)=(9-6√3+3)/(9-3)=(12-6√3)/6=2-√3
![( sqrt[8]{x} - sqrt[4]{y} )( sqrt[4]{x} + sqrt{y} + sqrt[8]{xy^2} )/ ( sqrt[8]{x} - sqrt[4]{y} )( sqrt[4]{x} + sqrt{y} + sqrt[8]{xy^2} )/](https://tex.z-dn.net/?f=%28+sqrt%5B8%5D%7Bx%7D+-+sqrt%5B4%5D%7By%7D+%29%28+sqrt%5B4%5D%7Bx%7D+%2B+sqrt%7By%7D+%2B+sqrt%5B8%5D%7Bxy%5E2%7D+%29%2F)
![( sqrt[4]{x} + sqrt{y} + sqrt[8]{xy^2} )= sqrt[8]{x} - sqrt[4]{y} ( sqrt[4]{x} + sqrt{y} + sqrt[8]{xy^2} )= sqrt[8]{x} - sqrt[4]{y}](https://tex.z-dn.net/?f=%28+sqrt%5B4%5D%7Bx%7D+%2B+sqrt%7By%7D+%2B+sqrt%5B8%5D%7Bxy%5E2%7D+%29%3D+sqrt%5B8%5D%7Bx%7D+-+sqrt%5B4%5D%7By%7D+)
6
√(2√5-3)²-√(2√5-3)²=|2√5-3|-|2√5+3|=2√5-3-2√5-3=-6
∛(9*375)=∛3(27*125)=3*5=15
2
3
x³-125=0
x³=125
x=5
a²-3a-4=0
a1+a2=3 U a1*a2=-4
a1=-1⇒
a2=4⇒
4
∛(12+4√5)*∛(12-4√5)=∛[(12+4√5)(12-4√5)]=∛(144-80)=∛64=4
5
(3-√3)/(3+√3)=(3-√3)²/(3-√3)(3+√3)=(9-6√3+3)/(9-3)=(12-6√3)/6=2-√3
6
√(2√5-3)²-√(2√5-3)²=|2√5-3|-|2√5+3|=2√5-3-2√5-3=-6
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