開方的疑問(10分)

這是因為開方*開方會將開方抵消
所以開方4*開方4=2,
是沒有可能有負數,因為開方-4是一個虛數
prove
a^m*a^n=a^(m+n)
當m=n=0.5時(a開方時)
a^m*a^n=a^0.5*a^0.5=a^(0.5*0.5)=a
所以開方4*開方4=4

如果而你的方式也會有邏輯上的錯誤(因你的意思便會4等於-4)
正如
x=-2
x^2=(-2)^2
x^2=4
x=4^0.5
x=2
因x=-2and x=2,所以2等於-2這顯然是不能成立的

the ONLY result of sqrt(4) is 2, i.e. the positive answer
if you would like to refer to the negative answer, you MUST include the negative sign, i.e. -sqrt(4)

in the equation x^2 = 4, since both square root can result in 4 when multiplied by itself, both 2 and -2 are the answers.

As a result, what you have to remember is: in the equation x^2 = a, the answers are sqrt(a) and -sqrt(a)
but when you are asked the result of sqrt(a), you MUST only give the positive one