Question

高一数学题~~急~~~长长长长~~~~~~~~~~~~~~~谢谢~~~~~~~~~

2根号5 * 三次根号2.5 * 六次根号20 怎么写 要过程 谢谢`~~

Answer 1

简单嘛!(“^”表“次方”，如“5^(1/2)”表示“5的2分之1次方”)

2根号5 = 5^(1/2)

三次根号2.5 =2.5^(1/3)=(5*0.5)^(1/3)=[5^(1/3)]*[0.5^(1/3)]

六次根号20 =20^(1/6) =(4*5)^(1/6)
因为4=2^2，所以 =[2^(1/3)]*[5^(1/6)]

故2根号5 * 三次根号2.5 * 六次根号20等于：
5^(1/2) * [5^(1/3)]*[0.5^(1/3)] * [2^(1/3)]*[5^(1/6)]

=[5^(1/2) * 5^(1/3) * 5^(1/6)] * 0.5^(1/3) * 2^(1/3)
= 5 * 2^(-1/3) * 2(1/3)
= 5 * 2^0
= 5 * 1
= 5

Answer 2

答案是5
2根号5等于6根号5的3次方
三次根号2.5等于5/2的2次方
所以原式等于6次根号下（5的3次方*5/2的2次方*20）计算得6次根号下5的6次方
则答案等于5