Square and Cube
The square of a positive number is twice as big as the cube of that number. What is the number?
Age
14 to 16
Challenge level
Problem
The square of a positive number is twice as big as the cube of that number.
What is the number?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $\frac12$
$x^2=2x^3$, so $x^2=\underbrace{2\times x}_{\text{must be }1}\times x^2$
$\therefore 2x=1\\
\Rightarrow x=\frac12$
(or $x^2=x^3=0\Rightarrow x=0$ - but $x$ should be positive.)