Cube Root Inequality
To solve the given question, we need to find two numbers that the cube root of 63 falls between. The cube root of a number, \(\sqrt[3]{x}\), is the number which, when multiplied by itself three times, gives the number \(x\).
First, we need to look for perfect cubes that are close to 63. We know that \(3^3 = 27\) and \(4^3 = 64\), therefore the cube root of 63 will be slightly less than 4, because 63 is just one less than 64.
Thus, \(\sqrt[3]{63}\) is greater than 3 but less than 4. The expression can be written as:
\[3 < \sqrt[3]{63} < 4\]
Consequently, the boxes should contain the numbers 3 and 4, respectively.
