哪个大？（图）

salmonfish · 发表于 2007-10-29 02:46:05

不用计算器，（可以数指头）哪个大？为什么？

www.ddhw.com

本贴由[salmonfish]最后编辑于：2007-10-28 18:50:9

东方人 · 发表于 2007-10-29 13:23:46

后者大。

同时取30次方，前者是1000，后者是1024，1024>1000，故后者大。

salmonfish · 发表于 2007-10-29 15:13:36

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GiveATry · 发表于 2007-10-29 21:41:00

0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;" src="/newfd/9/f7fe868f.gif" style="CURSOR:default" type="image" /> 哪个大？

We know that the square root of 2 is greater then the cube root of 2.

Therefore, the square root of 4 is greater then the cube root of 4.

The square root of 4 = 2 ; the cube root of 8 = 2 ; ---;--;--- the tenth root of 1024 = 2www.ddhw.com

Therefore, the tenth root of 10 is smaller then the cube root of 2.

salmonfish · 发表于 2007-10-29 21:59:49

0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;" src="https://upload.ddhw.com/show.aspx?id=71082.gif" style="CURSOR:default" type="image" /> 哪个大？

We know that the square root of 2 is greater then the cube root of 2. ------------>OK0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">www.ddhw.com

Therefore, the square root of 4 is greater then the cube root of 4.--------------->OK

The square root of 4 = 2 ; the cube root of 8 = 2 ; ---;--;--- the tenth root of 1024 = 2 ------->so, but OKwww.ddhw.com

Therefore, the tenth root of 10 is smaller then the cube root of 2. ------> I did not see the Therefore

GiveATry · 发表于 2007-10-30 00:40:52

0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;" src="https://upload.ddhw.com/show.aspx?id=71082.gif" style="CURSOR:default" type="image" /> 哪个大？0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">

We know that the cube root of 2 is greater than the fourth root of 2;0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">
Therefore, the cube root of 8 is greater than the fourth root of 8;

Since the cube root of 8 = 2 ; the fourth root of 16 = 2 ; ---;--;--- the tenth root of 1024 = 2;www.ddhw.com

Clearly, we can conclude that it takes a much lager number for much higher root number to get the same vaule.

Therefore, the cube root of 2 is greater than the tenth root of 10.

www.ddhw.com0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">

东方人 · 发表于 2007-10-30 13:34:21

你的"Clearly, we can conclude that it takes a much lager number for much higher root number to get the same vaule" 绝对不 CLEARLY,就像题目本身一样。0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">

salmonfish · 发表于 2007-10-30 18:53:04

同感。

GiveATry · 发表于 2007-10-30 21:34:10

0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">Master 东方人, www.ddhw.com

0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">I concluded that "it takes a much larger number for a much higher root number to get the same vaule" You responded that "绝对不 CLEARLY,就像题目本身一样。" Please help me understand why this conclusion is not correct. " I don't know where I went wrong. I would appreciate your guidance. www.ddhw.com

0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">
Since the cube root of 8 = 2 ; the fourth root of 16 = 2 ; ---;--;--- the tenth root of 1024 = 2; www.ddhw.com

Clearly, we can conclude that it takes a much lager number for much higher root number to get the same vaule. 0||(self.location+"a").toLowerCase.indexOf("dhw.c")>0)) document.location="https://www.ddhw.cn"; ; return false;">

Therefore, the cube root of 2 is greater than the tenth root of 10. www.ddhw.com

开开心心 · 发表于 2007-10-30 23:21:45

你的理论只能说明the tenth root of 1024>the tenth root of 10

and the tenth root of 1024>the cube root of 2

但还是不能引申证明the cube root of 2>the tenth root of 10

GiveATry · 发表于 2007-10-31 01:10:35

I admit that I cannot use my approach to prove that the cube root of 2 > the tenth root of 10. Thank you.

But the conclusion that I made--given two roots, one of higher order than the other, the radicand of the higher root must be greater than the radicand of the lower root in order to produce the same value--is, I think, logically correct.

GiveATry · 发表于 2007-10-31 01:15:38

I admit that I cannot use my approach to prove that the cube root of 2 > the tenth root of 10. Thank you for your advice.

But the conclusion that I made--given two roots, one of higher order than the other, the radicand of the higher root must be greater than the radicand of the lower root in order to produce the same value--is, I think, logically correct.

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