# Quod Erat Demonstrandum

## 2018/07/18

### 畫 y=x^(1/n)

Filed under: Additional / Applied Mathematics,mathematics,NSS — johnmayhk @ 12:57 下午
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$\sqrt[3]{4}-\sqrt[3]{3}$$\sqrt[3]{3}-\sqrt[3]{2}$

$\sqrt[3]{4}-\sqrt[3]{3} < \sqrt[3]{3}-\sqrt[3]{2}$

(a) 不用圖像，試用代數證明上式。
(b) 由開 3 次根推廣至開 n 次根的情況。
#玩玩系列
#高中

Geogebra

Desmos

$\frac{1}{1.58}=\frac{50}{79}$

$\frac{1}{1.62}=\frac{50}{81}$

$\frac{1}{1.6}=\frac{5}{8}$

$\frac{1}{1.59}=\frac{100}{159}$

## 3 則迴響 »

1. I think it is the default setting and how the default defines, for a<0, do we have: a^(m/n)=?=((sqrt n times of a))^m=?=(sqrt n times of (a^m)) ???

迴響 由 Simon YAU — 2018/08/04 @ 7:37 下午 | 回應

2. Check check the definition for, a<0, (a)^(t), where t can be irrational or rational and where the number is undefined. We do not have the power to define, only mathematicians can say it.

迴響 由 Simon YAU — 2018/08/04 @ 7:50 下午 | 回應

3. I check that something about multivalued, not one to one should be the answer. Look forward to hearing your opinions.

迴響 由 Simon YAU — 2018/08/04 @ 8:00 下午 | 回應