What is the difference between the positive square root of 64 and the cube root of 64?
To find the difference, I need to subtract one root from the other. But first, I need to simplify each root. The positive square root of 64 is the number that, when multiplied by itself, gives 64. I can think of some factors of 64, such as 8 and 8, or 16 and 4. But only 8 times 8 is a perfect square, so the positive square root of 64 is 8. The cube root of 64 is the number that, when raised to the third power, gives 64. I can think of some factors of 64, such as 4 and 16, or 8 and 8. But only 4 times 4 times 4 is a perfect cube, so the cube root of 64 is 4. Now I can subtract the roots: 8 minus 4 is 4. So the difference between the positive square root of 64 and the cube root of 64 is 4. 