2022年二次根式知识点总结和习题 .pdf
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1、41二次根式的知识点汇总知识点一:二次根式的概念形如(,二.1)的式子叫做二次根式。注:在二次根式中,被开放数可以是数,也可以是单项式、多项式、分式等代数式,但必须注意:因为负数没有平方根,所以一;二 I 是为二次根式的前提条件,如门,-,.次根式,而,等都不是二次根式。判断下列代数式中哪些是二次根式?x a2 2a 2,、-x(x 巩固2、下列各式中,是二次根式是(知识点二:取值范围1.二次根式有意义的条件:由二次根式的意义可知,当a 0 时,二;有意义,是二次根式,所以要使二次根式有意义,只要使被开方数大于或等于零即可。2.二次根式无意义的条件:因负数没有算术平方根,所以当 a(B)xV(
2、C)x _ 5(D)1、下列各式中,不是二次根式的是((A)X(B)x 30(D)b2 二等是例题2,-16,2J3-x巩固 使代数式一2有意义的x取值范围是()X 2A x=-2;B x 3 且x=-2;C.x 3,且x=2;D.x 3 且x2;知识点三:二次根式?卫(:二.)的非负性仁(一丄 I)表示 a 的算术平方根,也就是说,血说0)是一个非负数,即晶10(一;二.1)。注:因为二次根式 _ I)表示 a 的算术平方根,而正数的算术平方根是正数,0 的算术平方根是0,所以非负数(一?:二.)的算术平方根是非负数,即上 0(二丨),这个性质也就是非负数的算术平方根的性质,和绝对值、偶次方
3、类似。这个性质在解答题目时应用较多,如若 J-:11,则 a=0,b=0;若加:-,则 a=0,b=0;若丄;11,则 a=0,b=0。例题 已知厂、2-x?-Jx-2 T,则 二x知识点四:二次根式(,卫):的性质卅厂-;(一:_|)文字语言叙述为:一个非负数的算术平方根的平方等于这个非负数。注:二次根式的性质公式:川-(,二 I)是逆用平方根的定义得出的结论。上面的公式也1可以反过来应用:若则,如:?.0)-x a a C.、-2a=a,-2a D.(x+2 Jxy+y)说,x y)=-,x+Jy 4.在下列各式的化简中,化简正确的有()?.a3=a J a 5x Jx-x=4x J x
4、6a a=3a2ab 2b b A.1 个B.2 个.2 cm3 cm,那么能与它们组成直角三角形的第三条线11.化简J225 7.04=_,丁11721082=_ 12.计算:3“5a,2j10b=13.若最简二次根式2j5x2+1与J7x2-1是同类二次根式,则x=_ 1 14.把根式 a彳根号外的a移到根号内,得_.24+1=10.6 6 5.已知二条线段的长分别为A.1cmB?先 5cm C.5cmD6.已知an 时,.(n-m)2_,当a _ 时,3a 段的长是()、填空题(每题2 分,共 20 分)文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3
5、文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:C
6、K4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T
7、9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7
8、 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3
9、R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4
10、 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7
11、A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3615.二次根式一3.、3x与.2ax的和是一.个.二次根式,则正整数a的最小值为_ 其和为16.观察下列各式:2 2=2?2;3 3=F 3 3 8 a-1 3(2)若a,b=3,则?.ab w;2(3)若a,b=6,则.ab 3;根据以上三个命题所
12、提供的规律猜想:若a 9,则.ab w25.(6 分)阅读下面的解题过程,判断是否正确?若不正确,请写出正确的解答。已知m为实数,化简:_ 1 _ 解:原式=mJm m -m m=-m-1.-m 3 3;4.:;用n(n _2)的等式表达你所观察得到的解答题(共68 分)17.(5分)计算:a-18.(5分)计算:、2219.(5分)解方程:20.(5分)解不等式:21.(5分)已知:x-22.(5分)化简并求值1-2aa2a2(212 4 1-3 48)815x _80=4x 5,3.2(x-.3)_.、6(x 1)Q,求x22 4的值.x 23.(5 分)已知实数a 满足|2003 a|+
13、a-2004=8,贝 9 a-20032的值是多少?24.(5 分)已知正数a和b,有下列命题:(1)若a 2,则ab 5 C、x1 B、x 1 D、x 2 的是()2 x B、x+2 C、x 2 D、5、在下列根式中,不是最简二次根式的是(辱 D a2+l B、2x+1 C、0.1y 6、7、下面的等式总能成立的是(a=a B、a a=a2 C m 为实数,则整数m+4m+5 的值B、正整数C、正数)、a?b=ab D、ab=a?b 一定是()D、负数已知;的正确结果为(.y9、10、y 若代数式,(2 a)2+(a 4)2的值是常数 2,贝 U a 的取值范围是(a 4 B、a 2 C、2
14、 a0,化简二次根式文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5
15、I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档
16、编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4
17、L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y
18、10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 H
19、B9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8
20、N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I310A 0.12 B、18 C、1;11、如果最简根式3a 8 与 17 2a 围是()A x 10 C、x10 12、若实数 x、y 满足 x2+
21、y2 4x 2y+5=0,则、的值是()3y 厶/x B、3+2 C、3+2.2 D、3 2 2 二、填空题x 一 1 1、要使 Y 有意义,则 x 的取值范围是。#3 x 2、_ 若 Ja+4+Ja+2b 2=0,贝U ab=_。3、若 1 a2与.a2 1 都是二次根式,那么1 a2+a2 1=_ 4、若 y=1 2x+2x 1+(x 1)2,贝 H(x+y)2003=_。5、_ 若 迈 x1+寸 3 x,化简 p(x+2)2 3(x+3)3=_。6、_若.(a+1)2=.(a 1)2,贝 U a=.D、一75 是同类二次根式,那么使4a 2x 有意义的 x 的范x+y 文档编码:CK4L
22、10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y1
23、0T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB
24、9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N
25、7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN5N7A5I7I3文档编码:CK4L10T9Y10T7 HB9D3R8N7V4 ZN
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