# Solve Equations For y

Banned

#### TheJason

Staff member
Moderator
1.

$$\displaystyle y^{5} = 125$$

$$\displaystyle \sqrt[5]{y^{5}} = \sqrt[5]{125}$$

$$\displaystyle y = 5$$

However, there might be some nth root stuff. But this is the way it seemingly goes.

2.

$$\displaystyle y^{6} = 100$$

$$\displaystyle \sqrt[6]{y^{6}} = \sqrt[6]{100}$$

$$\displaystyle y = ?$$

Again, quite sure the answer is something more than one number

Last edited:
harpazo

#### harpazo

##### Pure Mathematics
Banned
1.

$$\displaystyle y^{5} = 125$$

$$\displaystyle \sqrt[5]{y^{5}} = \sqrt[5]{125}$$

$$\displaystyle y = 5$$

However, there might be some nth root stuff. But this is the way it seemingly goes.

2.

$$\displaystyle y^{6} = 100$$

$$\displaystyle \sqrt[6]{y^{6}} = \sqrt[6]{100}$$

$$\displaystyle y = ?$$

Again, quite sure the answer is something more than one number
I'm sure there is missing work in your reply. I give you credit for trying. Let Mark take it from here.

#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
$$\displaystyle y^5=125\left(\cos(2\pi k)+i\sin(2\pi k)\right)$$

By de Moivre:

$$\displaystyle y=5^{\Large\frac{3}{5}}\left(\cos\left(\frac{2\pi}{5}k\right)+i\sin\left(\frac{2\pi}{5}k\right)\right)$$ where $$\displaystyle k\in\{0,1,2,3,4\}$$

anemone and harpazo

#### harpazo

##### Pure Mathematics
Banned
$$\displaystyle y^5=125\left(\cos(2\pi k)+i\sin(2\pi k)\right)$$

By de Moivre:

$$\displaystyle y=5^{\Large\frac{3}{5}}\left(\cos\left(\frac{2\pi}{5}k\right)+i\sin\left(\frac{2\pi}{5}k\right)\right)$$ where $$\displaystyle k\in\{0,1,2,3,4\}$$
Does de Moivre pop up in calculus 1?