Based on the given information, what other measurements of the square and cube could we find?
A cube has side length 10 inches. Jada says the surface area of the cube is [math]600[/math]in[math]^2[/math], and Noah says the surface area of the cube is [math]3,600[/math]in[math]^2[/math]. Here is how each of them reasoned:[br][br][table][tr][td]Jada's Method:[/td][td]Noah's Method:[/td][/tr][tr][td][math]6\cdot10^2[/math][br][math]6\cdot100[/math][br][math]600[/math][/td][td][math]6\cdot10^2[/math][br][math]60^2[/math][br][math]3,600[/math][br][/td][/tr][/table][br]Do you agree with either of them? Explain your reasoning.[br]
Consider this equation: [math]\boxed{\phantom{3}}^2+\boxed{\phantom{3}}^2=\boxed{\phantom{3}}^2[/math]. An example of 3 different whole numbers that could go in the circles are 3, 4, and 5, since [math]3^2+4^2=5^2[/math]. (That is, [math]9+16=25[/math].)[br][br][br]Can you find a different set of 3 whole numbers that make the equation true?
How many sets of 3 different whole numbers can you find?
Can you find a set of 3 different whole numbers that make this equation true? [math]\boxed{\phantom{3}}^3+\boxed{\phantom{3}}^3=\boxed{\phantom{3}}^3[/math].
How about this one? [math]\boxed{\phantom{3}}^4+\boxed{\phantom{3}}^4=\boxed{\phantom{3}}^4[/math].
Once you have worked on this a little while, you can understand a problem that is famous in the history of math. (Alas, this space is too small to contain it.) If you are interested, consider doing some further research on [i]Fermat’s Last Theorem[/i].