综合实践:∵
,即
,
∴
的整数部分为2,
∴
的小数部分为
.
(1)求
的整数部分和小数部分;
(2)已知
的立方根是3,
的算术平方根是4,c是
的整数部分,求
的平方根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36e44cd21f1535d7506ef005c495042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ffaf5232b03547381e61f5915ce819.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6011af1246472cfa38d0a21a320ecac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de31a7b108b0fdc888133f701e7c79b3.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbaad5188525ed3faaeace7d934e72a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed719e560cfda94e447adc32729597b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50690dab38f4512eb72e18b7f86cf6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed88804acf1c129a77fbb1b04fa0b56.png)
更新时间:2024-05-26 05:32:11
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相似题推荐
解答题-问答题
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【推荐1】已知
均为实数,
的立方根是4,正数b的平方根分别是
与
,c是
的整数部分.求
的值?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba1e7a657ed134e68efd159b606620f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe74b1b723b856957896093fadd5da96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d7ee5df29f1b1da163d98181dc42b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad99c233faa1e9ca25a1e2d7b3014c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb1f865738e0be47387e19392dd7cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4cf6bb45abf82b5c6d4b390c246571.png)
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名校
【推荐2】解关于
,
的方程组
时,甲正确地解出
,乙因为把
抄错了,误解为
,求
的平方根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25fb34e3345b3c7532017578384f3fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a7a8b0f00bd6383e0fbca90889344b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646466a959ebff9c62eca9357db7ec1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1e4af9aba1baae3bf8c337750289adc.png)
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【推荐1】已知a+3的立方根是2,3a+b﹣1的平方根是±6,则a+2b的算术平方根是多少?
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解答题-作图题
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【推荐1】(1)比较大小:
+1
(填“>”、“<”或者“=”);
(2)在进行(1)的大小比较时,我们发现还可以利用数形结合法来解决问题,借助三角形三边关系,在方格纸上构造出以这三个数为三边的三角形,从而得出结论,请在图①中画出相应的图形(设小正方形的边长为1);
(3)用(2)中的方法在图②中画图比较大小:
(填“>”、“<”或者“=”).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
(2)在进行(1)的大小比较时,我们发现还可以利用数形结合法来解决问题,借助三角形三边关系,在方格纸上构造出以这三个数为三边的三角形,从而得出结论,请在图①中画出相应的图形(设小正方形的边长为1);
(3)用(2)中的方法在图②中画图比较大小:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8478b4682c4779f6a645ae5e3ed6e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://img.xkw.com/dksih/QBM/2021/6/1/2733385740288000/2798092246294528/STEM/adf4e46b735c476cb96e3f664db7237b.png?resizew=221)
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【推荐2】阅读下面的文字,解答问题:
材料一:大家知道
是无理数,而无理数是无限不循环小数,因此
的小数部分我们不可能全部地写出来,于是小明用
来表示
的小数部分,你同意小明的表示方法吗?事实上,小明的表示方法是有道理的,因为
的整数部分是1,将这个数减去其整数部分,差就是小数部分.由此我们得到一个真命题:
如果
,其中
是整数,且
那么
.
材料二:已知
是有理数,并且满足等式
求
的值.
解:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc17aaef97d9ce93544c9414375e74f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd31b4eca82585dd39d51297d0041584.png)
,解得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ddbb4ff15b25e5b7b35a1a7f557595.png)
请解答:
(1)如果
,其中
是整数,且
那么
_______,
______.
(2)如果
的小数部分为
,
的整数部分为
,求
的值;
(3)已知
是有理数,并且满足等式
,求
的值.
材料一:大家知道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34e01955f8c8fe2f0041b35d8d602a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff47c4e89e86e41c3c4351550cc16276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0171cdb6d0ccd9cf476c1a93238dda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f570a88863ec05afaee91ca00195a119.png)
材料二:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9e6ef88644629f8ae1a3a2633bf621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc17aaef97d9ce93544c9414375e74f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd31b4eca82585dd39d51297d0041584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57f3cbb2974964e4bafe60382f562cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ddbb4ff15b25e5b7b35a1a7f557595.png)
请解答:
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d81277d1d186ace2d5b90c99cedd85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6865e9c2df5ebb9fdb3335f590f8b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6aa18ec487c5e1f441da613b8d6bf62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb0dc71feeebc0b277b846dbb1c8f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a70ed9916b93a41e859474a45419f36.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edac77829e7aec29f8980f577959098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4c160faac60919e577e3a498d9e0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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解答题-问答题
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【推荐1】已知
的立方根是
,
的算术平方根是2,c是
的整数部分.
(1)求a,b,c的值;
(2)求
的平方根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b021815b9bb4aa6fe1839f40ef76c676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed719e560cfda94e447adc32729597b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50690dab38f4512eb72e18b7f86cf6f6.png)
(1)求a,b,c的值;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea7bbc7b259cd20c3fd8cef190280de.png)
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【推荐2】先阅读下面材料,再解答问题:
材料:任意一个有理数与无理数的和为无理数,任意一个不为零的有理数与一个无理数的积为无理数,而零与无理数的积为零.由此可得:若
,其中
,
为有理数,
是无理数,则
,
.
证明:∵
,
为有理数,
∴
是有理数,
∵
为有理数,
是无理数,
∴
,
∴
,
∴
.
(1)若
,其中
、
为有理数,则
,
;
(2)已知
的整数部分为
,小数部分为
,求
与
的值;
(3)在(2)的条件下,
,
为有理数,
,
,
,
满足
,求
,
的值.
材料:任意一个有理数与无理数的和为无理数,任意一个不为零的有理数与一个无理数的积为无理数,而零与无理数的积为零.由此可得:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b580d28a0155fbf7c358eadef3f95feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84dba41a7a4a57ca08a148e35e6971e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b580d28a0155fbf7c358eadef3f95feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c84e088e26df4551ccc2bc553b7f8ac.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84dba41a7a4a57ca08a148e35e6971e.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437672771d61c170cf6c01bc046e140f.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f250843edbfeff027d9454373be5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68c1d20a422a363e356a160f096503c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)在(2)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6f97073b4464172cf2e3c010f7955e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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