# Neat Number Trick

1. Nov 17, 2006

### sherlockjones

Hey all

Just thought I would share something I observed:

$$2 \sqrt[3]{8} = \sqrt[3]{64}$$

Or $$2 \sqrt[5]{10} = \sqrt[5]{320}$$

$$2^{5} \times 10 = 320 \rightarrow \sqrt[5]{320}$$

You raise the number outside to the power, and then multiply by the inside number.

Has this already been known?

Last edited: Nov 17, 2006
2. Nov 17, 2006

### chroot

Staff Emeritus
Yes, it's a pretty basic consequence of the way that exponents work.

$2 \cdot \left( 8 \right)^{1/3} = \left( {2^3 } \right)^{1/3} \cdot \left( 8 \right)^{1/3} = \left( {2^3 \cdot 8} \right)^{1/3} = \left( {64} \right)^{1/3}$

- Warren

3. Nov 17, 2006

### sherlockjones

wow I am an idiot. Thanks for pointing that out.

4. Nov 17, 2006

### chroot

Staff Emeritus
You're not an idiot at all. In fact, it'd be wonderful if every student was motivated to sit down and just explore math the way you just did. They'd learn so much more.

- Warren

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