# Neat Number Trick

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.

Last edited:

chroot
Staff Emeritus
Gold Member
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

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

chroot
Staff Emeritus