Did You Know About This Neat Number Trick?

[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?

 

[chroot]

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

 

[sherlockjones]

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

 

[chroot]

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