材料:如何将双重二次根式
(
,
,
)化简呢?如能找到两个数
,
(
,
),使得
,即
,且使
,即
,那么
,
,双重二次根式得以化简.
例如化简:
,
因为
且
,
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fdb78c3c82d7de7324a8c3c9e9fbd3.png)
由此对于任意一个二次根式只要可以将其化成
的形式,且能找到
,
(
,
),使得
,且
,那么这个双重二次根式一定可以化简为一个二次根式.
请同学们通过阅读上述材料,完成下列问题:
(1)填空:
= ,
= ;
(2)化简:
;
(3)计算:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79302e44ec001a6f493b466325e0e5aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d0b11699080909c77a3bc19753dc06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd54c10269786647f7f58245568831c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18bf676b743728833d21db05f7d55a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9a2c28054fd8e9930214f498f90000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49674a98f036ba592c7eb60e0d3700f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb1bde24adb7d8c05a5de93cde6192c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416a07357190aaf89ba9d46ecf7f9726.png)
例如化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fac3fe9e187a58f70691fb54e136eac.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17241c152c33b2f5e31cd90955b876b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9195069b3bba2b6fa60da9782a3a01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e528373eac4e6c178d68e5dad4f64893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fdb78c3c82d7de7324a8c3c9e9fbd3.png)
由此对于任意一个二次根式只要可以将其化成
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79302e44ec001a6f493b466325e0e5aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18bf676b743728833d21db05f7d55a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49674a98f036ba592c7eb60e0d3700f5.png)
请同学们通过阅读上述材料,完成下列问题:
(1)填空:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7eec0a5ed8b6a0e32cb9cec193bcad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba988c764bba864f053e17c485a22403.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441454f1d204d83f28288a31f7c76076.png)
(3)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f81f9276d6085715f53e8a2f6b11a1.png)
22-23八年级上·广西贵港·期末 查看更多[9]
广西壮族自治区贵港市港南区2022-2023学年八年级上学期期末数学试题(已下线)第1章 二次根式 章末检测卷-【帮课堂】2022-2023学年八年级数学下册同步精品讲义(浙教版)(已下线)第12章 二次根式(B卷·能力提升练)-【单元测试】2022-2023学年八年级数学下册分层训练AB卷(苏科版)(已下线)16.1 二次根式-2022-2023学年八年级数学下册《考点·题型·技巧》精讲与精练高分突破系列(人教版)(已下线)第十六章《二次根式》同步单元基础与培优高分必刷卷-2022-2023学年八年级数学下册《考点·题型·技巧》精讲与精练高分突破系列(人教版)(已下线)专题08 二次根式【知识梳理+专项训练】-2022-2023学年八年级数学下学期期中期末考点大串讲(苏科版)(已下线)核心考点08二次根式-【满分全攻略】2022-2023学年八年级数学下学期核心考点+重难点讲练与测试(苏科版)广西壮族自治区贵港市港北区港北区第六初级中学2022-2023学年八年级上学期期末数学试题第十六章 二次根式单元专项提升
更新时间:2024-02-16 20:06:15
|
相似题推荐
解答题-证明题
|
较难
(0.4)
解题方法
【推荐2】在
中,
,点
是直线
上一点,
,垂足为点
于点
,点
为
的中点,连接
.
![](https://img.xkw.com/dksih/QBM/2020/12/9/2610527237758976/2611905785905152/STEM/0db93452c81a45909b4a806749d0231b.png?resizew=123)
(1)如图1,如果
,且
在
边上,设
交
于点
,且
为
的中点,若
_________.
(2)如图2,如果
,且
在
边上,求证:
.
(3)如图3,如果
,且
在
的延长线上,
,请探究线段
之间的数量关系,并写出证明过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f2c48ec235694a8514517ea19b8cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96c51b170cf1637457b0d5236fd759f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://img.xkw.com/dksih/QBM/2020/12/9/2610527237758976/2611905785905152/STEM/311c67c6200e421d8aa2ae4b8c35712e.png?resizew=159)
![](https://img.xkw.com/dksih/QBM/2020/12/9/2610527237758976/2611905785905152/STEM/fc787b3993584caf8853b1858f7d7cf8.png?resizew=160)
![](https://img.xkw.com/dksih/QBM/2020/12/9/2610527237758976/2611905785905152/STEM/0db93452c81a45909b4a806749d0231b.png?resizew=123)
(1)如图1,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb6fd2fa53b92a03d21f208b74e3857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030e715bb10167189eb6fc91c0d25a99.png)
(2)如图2,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a355958abf7dc0f2eb949584cb87907b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42114784648f39b5dcb0eaa371aec4a.png)
(3)如图3,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d846d488fdef957b911bb295935852f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7b9d24a1685a636e92f5ae3d791b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fae050b733c5952e4dac7fb16b1839e.png)
您最近一年使用:0次