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1.二次根式定义:一般地,形如a~(1/2)(a≥0)的式子叫做二次根式,a叫做被开方数.注意:二次根式应满足以下两个条件:(1)形式上必须是a~(1/2)的形式;(2)被开方数a必须是非负数.2.积与商的算术平方根的性质积的算术平方根:(ab)~(1/2)=a~(1/2)·b~(1/2)(a≥0,b≥0);商的算术平方根:(a/b)~(1/2)=a~(1/2)/b~(1/2)(a≥0,b>0).注意:运用商的算术平方根的性质必须注意条件a≥0,b>0.特别注意b=0时,分式的分母为0,无意义.
1. Quadratic root definition: In general, the form of a ~ (1/2) (a ≥ 0) is called the quadratic root, a is called the square root. Note: The quadratic root should meet the following two conditions (2) The square a must be non-negative. (2) The square root of the product of the product of the square root of the product and the quotient: (ab) ~ ( 1/2) = a ~ (1/2) · b ~ (1/2) (a≥0, b≥0); arithmetical mean square of quotient: a / b ~ 1/2 = a ~ 1/2) / b ~ (1/2) (a≥0, b> 0). Note that the condition of the arithmetic square root of the quotient must be taken into account when the condition a ≥ 0, b> 0. Pay special attention to b = 0 The denominator is 0, meaningless.